tag:blogger.com,1999:blog-87567968547514490792024-03-14T01:56:48.770-07:00IBPSVimlesh Kumarhttp://www.blogger.com/profile/08177785010966710431noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8756796854751449079.post-83232077530625518642013-05-29T00:31:00.001-07:002013-05-29T00:35:39.765-07:00CUBE<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-size: medium;"><b><span style="text-decoration: none;"> </span><u>Cube</u></b></span></div>
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<span style="font-size: medium;"><u><b>Method
1:We will explain with a exmple.</b></u></span></div>
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<span style="font-size: medium;"><b>Ex:</b><span style="font-weight: normal;">Find
the cube of 51 i.e. </span><b>51^3</b></span></div>
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<span style="font-size: medium;"><b>Step
1:Cube ten's digit</b><span style="font-weight: normal;"> that means
5^3</span></span></div>
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<br /></div>
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<span style="font-size: medium;">125</span></div>
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<span style="font-size: medium;"><b>Step
2:</b><span style="font-weight: normal;"> </span><b>Compare the ratio</b><span style="font-weight: normal;">
between </span><b>Ten's Digit and Unit's Digit</b><span style="font-weight: normal;">
that means compare 5 ratio with 1 i.e. </span><b>5:1</b></span></div>
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<br /></div>
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<span style="font-size: medium;"><b>Now
we will write next digit to right hand side with ratio 5:1 </b></span>
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<span style="font-size: medium;"><b>125 25 5 1
------------First Row</b></span></div>
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<span style="font-size: medium;"><b>Step
3:Now Double the digit 2nd and 3rd from right hand side</b></span></div>
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<span style="font-size: medium;"><b> 50 10
----------Second Row</b></span></div>
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<span style="font-size: medium;"><b>Step
4:Add the First and Second Row</b></span></div>
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<span style="font-size: medium;"><b>125 25 5 1</b></span></div>
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<span style="font-size: medium;"><b> 50 10</b></span></div>
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<span style="font-size: medium;"><b>125 75 15 1</b></span></div>
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<span style="font-size: medium;"><b>132</b><span style="font-weight: normal;">(Add
Carry 7) </span><b>6</b><span style="font-weight: normal;">(Carry
7) </span><b>5</b><span style="font-weight: normal;">(Carrry 1 ) </span><b>1</b></span></div>
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<span style="font-size: medium;"><b>i.e</b></span></div>
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<br /></div>
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<span style="font-size: medium;"><b>51^3
= 132651</b></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTQawplCL79X4LBt-6FBtm24C3iy2npH40BDVrdTpUbGwFVMU3a_BZoDePmg4m9VizvOrKhmwg3PQS9P5h_AsG4LnOyb2kn5hJWtnDarPWmhEXgcCv70f9zM4N9wjET6JGvtM4QlWiahhA/s1600/Method+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="273" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTQawplCL79X4LBt-6FBtm24C3iy2npH40BDVrdTpUbGwFVMU3a_BZoDePmg4m9VizvOrKhmwg3PQS9P5h_AsG4LnOyb2kn5hJWtnDarPWmhEXgcCv70f9zM4N9wjET6JGvtM4QlWiahhA/s320/Method+2.png" width="320" /></a></div>
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<span style="font-size: medium;"><b><span style="text-decoration: none;">Method
2:</span><u>We will explain with a exmple.</u></b></span></div>
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<span style="font-size: medium;"><b>Ex:Find
the cube of 87 i.e. 87^3</b></span></div>
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<span style="font-size: medium;"><b>First(Ten)
Digit =8</b></span></div>
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<span style="font-size: medium;"><b>Second
(Unit)Digit=7</b></span></div>
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<br /></div>
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<span style="font-size: medium;"><u><b>Step
1:</b></u></span></div>
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<span style="font-size: medium;"><b>First
Row::</b><span style="font-weight: normal;">Write down the </span><b>Ten'</b><span style="font-weight: normal;">s
Digit </span><b>Cube</b><span style="font-weight: normal;">
</span><b>Square</b><span style="font-weight: normal;"> </span><b>Digit</b></span></div>
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<span style="font-size: medium;"><b>8^3 8^2 8 </b></span></div>
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<span style="font-size: medium;"><b>512 64 8 </b></span></div>
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<span style="font-size: medium;"><b>Second
Row::</b><span style="font-weight: normal;">Write down the </span><b>unit's</b><span style="font-weight: normal;">
Digit </span><b>Digit</b><span style="font-weight: normal;">
</span><b>Square</b><span style="font-weight: normal;"> </span><b>Cube
</b><span style="font-weight: normal;">from leave one place from left
handside.</span></span></div>
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<span style="font-size: medium;"><span style="font-weight: normal;"> </span><b>7 </b><span style="font-weight: normal;"> </span><b>7^2 </b><span style="font-weight: normal;"> </span><b>7^3</b></span></div>
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<span style="font-size: medium;"><b> 7 49 343</b></span></div>
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<span style="font-size: medium;"><b>Third
Row::Multiply</b><span style="font-weight: normal;"> 2nd and 3rd place
of First row and Second row </span><b>Then Add </b><span style="font-weight: normal;">First
Row and Second Row.</span></span></div>
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<span style="font-size: medium;">512 64 8</span></div>
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<span style="font-size: medium;"> *7 *49 343</span></div>
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<span style="font-size: medium;">512 448 392 343</span></div>
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<br /></div>
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<span style="font-size: medium;"><b>Four
Row:Multiply by 3</b><span style="font-weight: normal;"> (Because we
are doing cube) in the third row at 2nd and 3rd place digit.</span></span></div>
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<span style="font-size: medium;">512 448 392 343</span></div>
<div class="western" style="border-bottom: 1px solid #000000; border-left: none; border-right: none; border-top: none; font-weight: normal; margin-bottom: 0cm; padding-bottom: 0.07cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm; text-decoration: none;">
<span style="font-size: medium;"> *3 *3</span></div>
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<span style="font-size: medium;">512 1344 1176 343 </span></div>
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<span style="font-size: medium;"><b>658</b><span style="font-weight: normal;">(Add
146) </span><b>5</b><span style="font-weight: normal;">(Add
121 carry 146) </span><b>0</b><span style="font-weight: normal;">(Add
34 and Carry 121) </span><b>3</b><span style="font-weight: normal;">(carry
34)</span></span></div>
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<span style="font-size: medium;"><b>i;e</b></span></div>
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<span style="font-size: medium;"><b>87^3</b><span style="font-weight: normal;">=</span><b>658503</b></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZR6MjvcF6-vediBcyOnB01-hrrsbNKTvjYdLpzy2YYgt3nLhvv2R0QqwLVmirA_gfX0F7Mg9wYLP7W9MxUbscm3wC9CpeL6nDVLrfnfpFIWRj4K1U9cknIpbXdPy7fbCa0ZdG2oETY4gb/s1600/Method+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="127" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZR6MjvcF6-vediBcyOnB01-hrrsbNKTvjYdLpzy2YYgt3nLhvv2R0QqwLVmirA_gfX0F7Mg9wYLP7W9MxUbscm3wC9CpeL6nDVLrfnfpFIWRj4K1U9cknIpbXdPy7fbCa0ZdG2oETY4gb/s320/Method+1.png" width="320" /></a></div>
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Vimlesh Kumarhttp://www.blogger.com/profile/08177785010966710431noreply@blogger.com0tag:blogger.com,1999:blog-8756796854751449079.post-68785158304707148972013-05-28T05:59:00.002-07:002013-05-28T06:05:39.525-07:00Square Root & Cube Root <div dir="ltr" style="text-align: left;" trbidi="on">
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<div class="western" style="margin-bottom: 0cm;">
<b> <span style="font-size: medium;"><u>Square
Root and Cube Root</u></span> </b></div>
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<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<b><i>Shortcut Trick use for Perfect Square Root or Cube Root</i></b></div>
<table cellpadding="4" cellspacing="0" style="width: 435px;">
<colgroup><col width="63"></col>
<col width="45"></col>
<col width="121"></col>
<col width="64"></col>
<col width="101"></col>
</colgroup><tbody>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0.1cm;" width="63">
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<b>Number</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0.1cm;" width="45">
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<b>Square<br /> </b>
</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0.1cm;" width="121">
<div class="western">
<b>Last Digit of its Square Root</b></div>
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<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0.1cm;" width="64">
<div class="western">
<b>Cube</b></div>
</td>
<td style="border: 1px solid #000000; padding: 0.1cm;" width="101">
<div class="western">
<b>Last Digit of its Cube Root</b></div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
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1</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
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<b>1</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
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1</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="64">
<div class="western">
<b>1</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
1</div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
<div class="western" style="font-weight: normal;">
2</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
<div class="western">
<b>4</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
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4</div>
</td>
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<div class="western">
<b>8</b></div>
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<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
8</div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
<div class="western" style="font-weight: normal;">
3</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
<div class="western">
<b>9</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
<div class="western" style="font-weight: normal;">
9</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="64">
<div class="western" style="font-weight: normal;">
2<b>7</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
7</div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
<div class="western" style="font-weight: normal;">
4</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
<div class="western" style="font-weight: normal;">
1<b>6</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
<div class="western" style="font-weight: normal;">
6</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="64">
<div class="western" style="font-weight: normal;">
6<b>4</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
4</div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
<div class="western" style="font-weight: normal;">
5</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
<div class="western" style="font-weight: normal;">
2<b>5</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
<div class="western" style="font-weight: normal;">
5</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="64">
<div class="western" style="font-weight: normal;">
12<b>5</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
5</div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
<div class="western" style="font-weight: normal;">
6</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
<div class="western" style="font-weight: normal;">
3<b>6</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
<div class="western" style="font-weight: normal;">
6</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="64">
<div class="western" style="font-weight: normal;">
21<b>6</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
6</div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
<div class="western" style="font-weight: normal;">
7</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
<div class="western" style="font-weight: normal;">
4<b>9</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
<div class="western" style="font-weight: normal;">
9</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="64">
<div class="western" style="font-weight: normal;">
34<b>3</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
3</div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
<div class="western" style="font-weight: normal;">
8</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
<div class="western" style="font-weight: normal;">
6<b>4</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
<div class="western" style="font-weight: normal;">
4</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="64">
<div class="western" style="font-weight: normal;">
51<b>2</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
2</div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
<div class="western" style="font-weight: normal;">
9</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
<div class="western" style="font-weight: normal;">
8<b>1</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
<div class="western" style="font-weight: normal;">
1</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="64">
<div class="western" style="font-weight: normal;">
72<b>9</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
9</div>
</td>
</tr>
<tr valign="TOP">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="63">
<div class="western" style="font-weight: normal;">
10</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="45">
<div class="western" style="font-weight: normal;">
10<b>0</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="121">
<div class="western" style="font-weight: normal;">
0</div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm; padding-top: 0cm;" width="64">
<div class="western" style="font-weight: normal;">
100<b>0</b></div>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm; padding-top: 0cm;" width="101">
<div class="western" style="font-weight: normal;">
0</div>
</td>
</tr>
</tbody></table>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<u><b>Observation</b></u></div>
<div class="western" style="margin-bottom: 0cm;">
<b>1.</b>If the unit
digit of any number is <b>2 or 8</b> then its <b>square</b> will have
unit digit as <b>4</b>.</div>
<div class="western" style="margin-bottom: 0cm;">
<b>2</b>.If the unit
digit of any number is <b>3 or 7</b> then its <b>square</b> will have
unit digit as <b>9</b>.</div>
<div class="western" style="margin-bottom: 0cm;">
<b>3</b>.If the unit
digit of any number is <b>4 or 6</b> then its <b>square</b> will have
unit digit as <b>6</b>.</div>
<div class="western" style="margin-bottom: 0cm;">
<b>4</b>.If the unit
digit of any number is <b>1 or 9</b> then its<b> square</b> will have
unit digit as <b>1.</b></div>
<div class="western" style="margin-bottom: 0cm;">
<b>5</b>.If the unit
digit of any number is <b>0</b> then its <b>square</b> will have unit
digit as <b>0</b>.</div>
<div class="western" style="margin-bottom: 0cm;">
<b>Example</b></div>
<div class="western" style="margin-bottom: 0cm;">
<b>1.Find the square
root of 529</b></div>
<div class="western" style="margin-bottom: 0cm;">
5,29(Last two digit)
</div>
<div class="western" style="margin-bottom: 0cm;">
3..............9</div>
<div class="western" style="margin-bottom: 0cm;">
7..............9</div>
<div class="western" style="margin-bottom: 0cm;">
3/7</div>
<div class="western" style="margin-bottom: 0cm;">
5</div>
<div class="western" style="margin-bottom: 0cm;">
5 is between 2 & 3</div>
<div class="western" style="margin-bottom: 0cm;">
So value is 2</div>
<div class="western" style="margin-bottom: 0cm;">
2 * 3=6</div>
<div class="western" style="margin-bottom: 0cm;">
As compare 5 with 6 ,So
5 is less than 6 so value of unit is 3(i.e Smaller)</div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
Now, Square Root of 529
is <b>23</b></div>
<div class="western" style="margin-bottom: 0cm;">
<b>2.Find the square
root of </b>6084</div>
<div class="western" style="margin-bottom: 0cm;">
60,84(Last two digit)
</div>
<div class="western" style="margin-bottom: 0cm;">
2..............4</div>
<div class="western" style="margin-bottom: 0cm;">
8..............4</div>
<div class="western" style="margin-bottom: 0cm;">
2/8</div>
<div class="western" style="margin-bottom: 0cm;">
60</div>
<div class="western" style="margin-bottom: 0cm;">
60 is between 49 &
64</div>
<div class="western" style="margin-bottom: 0cm;">
So value is 7</div>
<div class="western" style="margin-bottom: 0cm;">
7 * 8=56</div>
<div class="western" style="margin-bottom: 0cm;">
As compare 56 with 60
,So 60 is large than 56 so value of unit is 8(i.e Larger unit digit)</div>
<div class="western" style="margin-bottom: 0cm;">
Now, Square Root of 529
is <b>78</b></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<u><b>Square Root</b></u></div>
<ol>
<li><div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;">First
Find the <b>last digit</b> of the <span style="font-size: medium;">square</span> root ,which can directly be
obtained by looking the last digit of the number and then referring
the table.</span></div>
</li>
<li><div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;">Next,Ignore
the <b>last 2 digits of the number</b> and look at the number which
remain. Think of a number ,whose <b><span style="font-size: medium;">square</span> is just equal or less
</b>then this remaining number.</span></div>
</li>
</ol>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><b>Ex:Find
the Square Root of 10 24.</b></span></div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;">Last Digit
of 1024 is <b>4</b></span></div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><b>According
to Above Table</b></span></div>
<div class="western" style="font-weight: normal; margin-bottom: 0cm;">
<span style="font-size: medium;">2........................................................4</span></div>
<div class="western" style="font-weight: normal; margin-bottom: 0cm;">
<span style="font-size: medium;">8........................................................4</span></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><b>Ignore
the Last two digit that is 24</b></span></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><b>Now
Focus on 10</b></span></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><b>Now
find the square of number which is equal or lesser than 10.</b></span></div>
<div class="western" style="font-weight: normal; margin-bottom: 0cm;">
<span style="font-size: medium;">3^2=9</span></div>
<div class="western" style="font-weight: normal; margin-bottom: 0cm;">
<span style="font-size: medium;">4^2=16</span></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="font-weight: normal; margin-bottom: 0cm;">
<span style="font-size: medium;">From
here we find square of 3 is less than to 10.</span></div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><span style="font-weight: normal;">So,This
is the ten's digit of square root is </span><b>3</b></span></div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><span style="font-weight: normal;">Now
9 (</span><b>Smaller than 10 ,so we will choose small digit i.e. 2</b><span style="font-weight: normal;">)
is less than 10 that why unit digit is </span><b>2.</b></span></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><span style="font-weight: normal;">Now
,Answer of</span><b> square root </b><span style="font-weight: normal;">of</span><b>
1024 </b><span style="font-weight: normal;">is</span><b> 32.</b></span></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><u><b>Cube
Root</b></u></span></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;">This
technique helps you find out the cube root of a 4 or 5 or 6 digits
number mentally.<br /><br /><b>Note:</b></span></div>
<ol>
<li><div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;">Cube
of a <b>2-digit number</b> will have at <b>max 6 digits </b>(88^3 =
681,472). That implies if you are given with a 6 digit number, its
cube root will have 2 digits.</span></div>
</li>
<li><div class="western" style="margin-bottom: 0cm;">
<strong> </strong><span style="font-size: medium;">This
trick works only for <b>perfect cubes</b>, it will not work for any
arbitrary 6-digit</span></div>
</li>
<li><div class="western" style="margin-bottom: 0cm;">
<strong> </strong><span style="font-size: medium;">It
works only for<b> integers</b></span></div>
</li>
</ol>
<u><b>Example:</b></u><span style="font-size: medium;"> </span><br />
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;">Say
you have to find the cube root of <strong>166375</strong>. It is
known that it’s a perfect cube.<u><b> </b></u></span></div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><u><b>Step
1:</b></u> </span></div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;">Now
<b>divide this number into two parts.</b> The <b>right hand side
</b>should always have <b>3 digits</b>. <b>Remaining digits</b> will
<br />come in left hand side. Do it as shown
below.<br /><b>166</b><strong>.........................................375</strong><br /><br />You
know the answer will have <b>2 digits</b>. Digit at tens place and
digit at units place. We will get the digit at <b>tens place</b>
using the <b>left hand side </b>of the original number (166) and
digit at <b>units place</b> using <b>right hand side</b> of the
number (375)</span></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
</div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><strong><u>Step
2. </u></strong><br />For l<b>eft hand side</b> we need to use <b>Above
Table</b> . We have to see the above table in which <b>166</b> lies
between <b>125</b> and <b>216</b>. So we will take the cube root of
the smaller number i.e. <b>125</b> which is <b>5</b>.<br /><br />So <b>5</b>
is the <b>tens digit</b> of the answer.<br /><strong><u>Step 3.</u></strong><strong>
</strong><br />For right hand side we need to use Above Table. Since
our <b>original number</b> (the perfect cube) <b>ends in 5</b> (see
16637<b>5</b><strong>), </strong>its cube root will ends in 5.<br />Thus
the <b>units digit </b>will be <b>5</b>.</span></div>
<div class="western" style="margin-bottom: 0cm;">
<br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><u><b>Step
4:</b></u><br />Combining the results we get the answer as <b>55</b>.</span><br />
</div>
<div class="western" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><br /></span><b>(166375)^1/3</b>
= <b>55</b></div>
</div>
Vimlesh Kumarhttp://www.blogger.com/profile/08177785010966710431noreply@blogger.com0tag:blogger.com,1999:blog-8756796854751449079.post-22793069941665913302013-05-27T00:32:00.000-07:002013-05-27T03:47:50.111-07:00MULTIPLICATION<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-size: large;"><u><b>Multiplication</b></u></span><span style="font-size: large;">
</span><span style="font-size: large;"><u><b>Trick</b></u></span></div>
<u><b>Method 1 :</b></u><b>Multiplication of 2 Digit Numbers</b>
Where the <b>first digit</b> of both numbers is <b>same</b> and <b>Last
digit of the 2 Numbers sum to 10</b>.<br />
(1)56*54<br />
First Digit of <b>5</b>6 is <b>5</b><br />
First Digit of <b>5</b>4 is <b>5</b><br />
<br />
<br />
Last Digit of 5<b>6</b> is 6<br />
Last Digit Of 5<b>4</b> is 4<br />
<b>Sum</b> of Last Two digit is <b>6+4</b>=10<br />
<br />
<br />
<br />
<b>Multiply of 5 and (5+1)</b><br />
5*(5+1)=5*6=30 Write Down 30<br />
<b>Multiply of Last Digit of Both Numbers</b><br />
6*4=24 write Down 24<br />
i.e<br />
<b>56*54</b>=<b>3024</b><br />
<br />
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<br />
<div class="western" style="margin-bottom: 0cm;">
<b> OR</b></div>
<div class="western">
<span style="font-size: medium;"><u><span style="font-weight: normal;">Multiplication
of 2 Digit Number the</span><b> Ten's Digit Add up to 10 </b><span style="font-weight: normal;">and
</span><b>Unit digits Same</b></u></span></div>
<div class="western" style="font-weight: normal;">
<span style="font-size: medium;">1.First
Find the multiplication of last two digit of both the numbers</span></div>
<div class="western" style="font-weight: normal;">
<span style="font-size: medium;">2.Multiply
the Ten's Digits and Add the Common Digit to the multiplication</span></div>
<div class="western">
<b>Ex:44 * 64</b></div>
<div class="western">
First Number is 44</div>
<div class="western">
First Digit of 44 is 4</div>
<div class="western">
Second Digit of 44 is 4
</div>
<div class="western">
Second Number is 64</div>
<div class="western">
First Digit of 64 is 6</div>
<div class="western">
Second Digit of 64 is 4</div>
<div class="western">
Second Digit in Both Number is Same i.e 4</div>
<div class="western">
<b>Sum of First Digit of Both Number is</b>
4+6=10</div>
<div class="western">
<b>Multiplying the unit Digit </b>,we get
4*4=<b>16</b>,Put it at <b>right hand side.</b></div>
<div class="western">
<b>Multiplying the Ten's Digits of Both Number</b>
and <b>Adding Common Digit</b> ,we get (4*6) + 4=24+4=28 ,Put it at
the <b>left hand side.</b></div>
<div class="western">
<b>So,We get Answer is 2816</b></div>
<br />
<br />
<u><b>Method 2 :</b></u>Multiplication of two digit number that
<b>differ by 6</b><br />
<b>(1)10*16</b><br />
<b>First</b> Number =<b>10</b><br />
<b>Second</b> Number =<b>16</b><br />
<b>Difference</b> Between <b>10</b> & <b>16</b> is 16-10=<b>6</b>
<br />
If two number differ by 6 then their product is the <b>square of
their average </b> <b>minus 9</b> .<br />
<b>Average of 10 and 16</b> is (10+16)/2=26/2=<b>13</b><br />
<b>Square of Average Number</b><br />
13^2 =<b>169</b><br />
<b>Minus 9</b> from Square of average
<br />
169<b>-9</b>=<b>160</b><br />
<b>i.e</b><br />
10*16=<b>160</b><br />
<br />
<br />
<br />
<u><b>Method 3 :</b></u>Multiplication of two digit number that
<b>differ by 4</b><br />
<b>(1)10*14</b><br />
<b>First</b> Number =<b>10</b><br />
<b>Second</b> Number =<b>14</b><br />
<b>Difference</b> Between <b>10</b> & <b>14</b> is 14-10=<b>4</b>
<br />
If two number differ by 6 then their product is the <b>square of
their average </b> <b>minus 4</b> .<br />
<b>Average of 10 and 14</b> is (10+14)/2=24/2=<b>12</b><br />
<b>Square of Average Number</b><br />
12^2 =<b>144</b><br />
<b>Minus 4</b> from Square of average
<br />
<b>144-4</b>=<b>140</b><br />
<b>i.e</b><br />
10*14=<b>140</b><br />
<br />
<u><b>Method 4 :</b></u>Multiplication of two digit number that
<b>differ by2</b><br />
<b>(1)10*12</b><br />
<b>First</b> Number =<b>10</b><br />
<b>Second</b> Number =<b>12</b><br />
<b>Difference</b> Between <b>10</b> & <b>12</b> is 12-10=<b>2</b>
<br />
If two number differ by 6 then their product is the <b>square of
their average </b> <b>minus 1</b> .<br />
<b>Average of 10 and 12</b> is (10+12)/2=22/2=<b>11</b><br />
<b>Square of Average Number</b><br />
11^2 =<b>121</b><br />
<b>Minus 1</b> from Square of average
<br />
121<b>-1</b>=<b>120</b><br />
<b>i.e</b><br />
10*12=<b>120</b><br />
<u><b>Method 5 :</b></u>Multiplication of <b>125 </b>with Any Number.<br />
(1)92*125<br />
<b>125</b>=5^3=(10/2)^3=1000/8<br />
<b>Now</b>,<br />
92*125 <br />
92*(1000/8) <br />
(92*1000)/8<br />
92000/8<br />
<b>11500</b><br />
<b>i.e</b><br />
<b>92*125</b>=<b>11500</b><br />
<br />
<u><b>Method 6 :</b></u>Multiplication of <b>25 </b>with Any Number.<br />
(1)92*25<br />
<b>25</b>=5^2=(10/2)^2=100/4<br />
<b>Now</b>,<br />
92*25 <br />
92*(100/4) <br />
(92*100)/4<br />
9200/4<br />
<b>2300</b><br />
<b>i.e</b><br />
<b>92*25</b>=<b>2300</b><br />
<br />
<u><b>Method 7 :</b></u>Multiplication of <b>5 </b>with Any Number.<br />
(1)92*5<br />
<b>5</b>=5^1=(10/2)^1=10/2<br />
<b>Now</b>,<br />
92*5 <br />
92*(10/2) <br />
(92*10)/2<br />
920/2<br />
<b>460</b><br />
<b>i.e</b><br />
<b>92*5</b>=<b>460</b><br />
<br />
<br />
<u><b>Method 8 :</b></u>Multiplication of <b>999 </b>with Any Number.<br />
(1)92*999<br />
<b>999</b>=1000-1<br />
<b>Now</b>,<br />
92*999<br />
92*(1000-1) <br />
(92*1000)-(92*1)<br />
92000-92<br />
<b>91908</b><br />
<b>i.e</b><br />
<b>92*999</b>=<b>91908</b><br />
<br />
<u><b>Method 9 :</b></u>Multiplication of <b>99 </b>with Any Number.<br />
(1)92*99<br />
<b>99</b>=100-1<br />
<b>Now</b>,<br />
92*99<br />
92*(100-1) <br />
(92*100)-(92*1)<br />
9200-92<br />
<b>9108</b><br />
<b>i.e</b><br />
<b>92*99</b>=<b>9108</b><br />
<br />
<br />
<u><b>Method 10 :</b></u>Multiplication of <b>9 </b>with Any Number.<br />
(1)92*99<br />
<b>9</b>=10-1<br />
<b>Now</b>,<br />
92*9<br />
92*(10-1) <br />
(92*10)-(92*1)<br />
920-92<br />
<b>828</b><br />
<b>i.e</b><br />
<b>92*9</b>=<b>828</b><br />
<br />
<u><b>Method 11 :</b></u>Multiplication of <b>11 </b>with Any Number.<br />
(1)92*11<br />
Write down 0 at the both end of Number(it is called <b>Zero Sandwich </b>)<br />
0920<br />
sum of the two successive number digit<br />
0+9....9+2....2+0<br />
9...11....2<br />
10.....1(carry 1)....2<br />
<br />
1012 <br />
<b>i.e</b><b>92*11</b>=<b>1012</b><br />
<b> OR</b><br />
Insert the <b>sum of 2 successive</b> digits and to put <b>2 terminal digit in its place</b> <br />
<br />
456872*11<br />
<b>Put Two Terminal Digits in its place </b><br />
<b>4</b>.........................................................................<b>2</b><br />
<b><br /></b>
<b>Insert the Sum of 2 Successive digit</b><br />
4....(<b>4+5</b>).....(<b>5+6</b>)....(<b>6+8</b>)....(<b>8+7</b>).....(<b>7+2</b>).......2<b><br /></b><br />
4.....<b>9</b>......<b>11</b>.......<b>14</b>......<b>15</b>.....<b>9</b>.....2<b> </b><br />
<b> 4.....9+1</b>(Take Carry 1)......<b>11-10</b>(10 Carry Forwarded to left hand-side)<b>+1</b>(Carry take 1 from Right hand side).....<b>14-10</b>(10 Carry Forwarded to left hand-side)<b>+1</b>......<b>15-10</b>(10 Carry Forwarded to left hand-side).....9....2<br />
4...........10.............2..............4+1...............5.........9...........2<br />
4+1........10-10...........2...............5................5.........9..........2 <br />
<b> 5</b>..................0..............2...........5.......5...........9..........2<br />
5025592<br />
<b>i.e</b> <b> </b><br />
456872*11=5025592<br />
<u><b>Note:</b></u> if sum of two digit is greater than 10 then add 1 to previous digit and subtract 10 to the associate digit <br />
<br />
<br />
<br />
<u><b>Method 12 :</b></u>Multiplication of <b>12 </b>with Any Number.<br />
(1)65214*12<br />
Write down 0 at the both end of Number(it is called <b>Zero Sandwich </b>)<br />
<b>0</b>65214<b>0</b><br />
The <b>Ultimate Digit </b>is <b>0</b> and the <b>Penultimate</b> digit is <b>4</b> .<br />
<b>Adding</b> the <b>ultimate digit</b> and <b>twice the penultimate digit</b> we get <b>0+8</b>=<b>8</b><br />
<br />
For the <b>Ten's Column </b>,The <b>ultimate </b>digit is <b>4</b> and the <b>Penultimate</b> digit is <b>1</b> so <b>4+2</b>=6<br />
<br />
Like wise 1+4=5 and 2+10=12 ,with <b>12</b> We <b>set down 2</b> and <b>carry 1</b>.<br />
5+12+carry1=18 and again <b>we carry 1</b>.<br />
<br />
The Final step is 6+0+<b>carry 1</b>=7<br />
<br />
So ,the Answer is <b>782568</b> <br />
<br />
<u><b>Method 13 :</b></u>Multiplication of Any two Number, Both Ranging between 11 to 19.<br />
<br />
<b>(1)</b>13*19<br />
Add First Number and Last digit of second number Take 0 (Zero) in the third place of this number the add product of last digit of the two numbers in it.<br />
<br />
<b>First</b> Number is <b>13</b><br />
<b>Second</b> Number is <b>19</b><br />
<br />
<b>Add First Number and Last Digit of Second Number</b><br />
First Number is <b>13</b><br />
Second digit of second number is <b>9</b><br />
13+9=<b>22</b><br />
<br />
<b>Put 0 (Zero)</b><br />
0<br />
<br />
<b>Product of Last Digit of two Number.</b><br />
Last Digit of 13 is <b>3</b><br />
Last digit of 19 is <b>9</b><br />
3*9=<b>27</b><br />
<br />
<b>Add Product of Last Digit of two Number in Number</b><br />
22.....0 <b>+ 27</b><br />
<b>220</b>+27<br />
447 <br />
<b>i.e.</b><br />
13*19=<b>447</b><br />
<br />
<br /></div>
Vimlesh Kumarhttp://www.blogger.com/profile/08177785010966710431noreply@blogger.com0tag:blogger.com,1999:blog-8756796854751449079.post-90568227843406113562013-05-24T00:34:00.003-07:002013-09-07T02:50:02.775-07:00SQUARE<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-size: large;"><b> </b><u><b>Square of 2 Digit</b></u></span><br />
<br />
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<div align="LEFT" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><u><b>Method
1:</b></u></span><span style="font-size: medium;">If </span><span style="font-size: medium;"><b>unit
digit is 5 </b></span><span style="font-size: medium;">then,</span><br />
(25)^2<br />
That
Means<br />
<br />
2 5<br />
<u><b>Add 1 </b></u><br />
<b>2</b>+<b>1</b>(Add
1 More)=<b>3</b><br />
<br />
<u><b>Square of unit Digit</b></u><br />
5^2 =
<b>25</b><br />
<br />
<u><b>Now</b></u><br />
2*3=<b>6</b><br />
<br />
(25)^2=625<br />
<br />
<span style="font-size: medium;"><u><b>Method
2:</b></u></span><span style="font-size: medium;">Let me explain
this trick by taking examples</span><br />
67^2 = [<b>6</b>^2] [<b>7</b>^2]
<b>+</b> <b>20</b>*<b>6</b>*<b>7</b> = 3649+840 = 4489<br />
similarly<br />
25^2
= [2^2][5^2]+20*2*5 = 425+200 = 625</div>
<h2 align="LEFT" class="western">
<span style="font-size: medium;"><u>Method
3:</u><span style="font-weight: normal;">Square of any 2 digit number </span></span>
</h2>
<dl>
<dt style="text-align: left;">Let me explain this rule by taking
examples<br />27^2 = (<b>27+3</b>)*(<b>27-3</b>) + <b>3^2</b> = 30*24
+ 9 = 720+9 = 729<br />In this method, we have <b>to make a number
ending with 0</b>, that's why; we add 3 to 27.
</dt>
<dt style="text-align: left;">
</dt>
<dt style="text-align: left;">
<u><b>1 more example</b></u><br />78^2 = (78+2)*(78-2) + 2^2 = 80*76 +
4 = 6080+4 = 6084
</dt>
</dl>
<h2 align="LEFT" class="western">
<span style="font-size: medium;"><u>Method 4:</u><span style="font-weight: normal;">Square
of any 2 digit number </span></span>
</h2>
<dl><dd style="text-align: left;">The Method is to use (a+b)^2 Formula in
the following Manner <b>a^2</b> / <b>2ab</b> /<b>b^2</b></dd>
<dt style="margin-bottom: 0.5cm; text-align: left;">
(1)85^2</dt>
<dd style="margin-bottom: 0.5cm; text-align: left;">8 5 Break in two part 8 & 5</dd><dd style="margin-bottom: 0.5cm; text-align: left;">8^2....... 2*8*5......... 5^2 (square of 8 <b>/</b> 2 * 8 *5
<b>/</b> square of 5)</dd><dd style="margin-bottom: 0.5cm; text-align: left;">64...............80...............25</dd><dd style="margin-bottom: 0.5cm; text-align: left;">64..............82................5(Carry 2)
</dd><dd style="margin-bottom: 0.5cm; text-align: left;">72..............2(Carry 8).............5</dd><dd style="margin-bottom: 0.5cm; text-align: left;">7225</dd><dd style="margin-bottom: 0.5cm; text-align: left;">i.e
</dd><dd style="margin-bottom: 0.5cm; text-align: left;"><b>85^2</b>=<b>7225</b></dd><dd style="margin-bottom: 0.5cm; text-align: left;"></dd></dl>
<div align="LEFT" style="margin-bottom: 0cm;">
<span style="font-size: medium;"><u><b>Method 5:</b></u></span><span style="font-size: medium;"><b>Square
of numbers near to 50</b></span><br />
Let me explain this rule by
taking examples<br />
<b>(1)37^2 :-</b><br />
37 is the near by 50 so,
First Calculate 50-37 ,it is 13<br />
<b>13 </b>is less than 50
,Therefore <b>deduct 13 from 25 </b>i.e. <b>25-13(How Much Less)
</b><br />
25-13=12 <br />
13^2=169<br />
Now <br />
12.....<b>1</b>69 (carry 1
)<b><br /></b><br />
<b>37^2=1369 </b><br />
<br />
<b>(2)57^2 :-</b><br />
57 is
the near by 50 so, First Calculate 50+7(<b>How Much More</b>). <br />
<b>7
</b>is greater than 50 therefore <b>Add 7 to 25 </b>i.e. <b>25+7
</b><br />
25+7=32 <br />
7^2=49<br />
Now <br />
32.....49 (No carry
)<b><br /></b><br />
<b>57^2=3249 </b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br />
<span style="font-size: medium;"><u><b>Method
6:</b></u></span><span style="font-size: medium;"><b>Square of
numbers near to 100</b></span><br />
Let me explain this rule by taking
examples<br />
<b>(1)96^2 :-</b><br />
First calculate 100-96, it is 4(<b>How
Much Less</b>)<br />
<br />
<b>4 </b>is less than 100 ,Therefore <b>deduct
4 from 96 </b>i.e. <b>96-4=</b>92 <br />
4^2=16<br />
We should written 16
As <b>16</b><br />
Now <br />
92.....16 (No carry )<b><br /></b><br />
<b>96^2=9216
</b><br />
(2)<b>115^2</b><br />
115 is the near by 100 so, First Calculate
100+15(<b>How Much More</b>). <b>15 </b>is greater than 100
therefore <b>Add 15 to 115 </b>i.e. <b>115+15 </b><br />
115+15=130
<br />
15^2=225<br />
Now <br />
130.....<b>2</b>25 (Carry 2)<b><br /></b><br />
<b>115^2=13225
</b>
</div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b> </b><span style="font-size: medium;"><u><b>Square
of <span style="font-size: medium;">Containing</span> <span style="font-size: medium;">Repeated</span> Number</b></u></span></div>
<div align="LEFT" style="margin-bottom: 0cm; text-decoration: none;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm; text-decoration: none;">
<span style="font-size: medium;"><b><u>Method
1 :</u><span style="font-size: medium;">Repetition</span> of 1</b></span></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b><br />Step 1:Count the
digit,Count=N</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>Step 2:Now starting From
1 Write The Number till N</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>Step 3 :Now Starting From
N Write number till 1</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>Ex: 11111^2</b></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
First
we See that there are 5 times 1</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
Now we
Write number from 1 to 5</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
Now
Again From From 5 to 1.</div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>So Answer is 123454321</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm; text-decoration: none;">
<span style="font-size: medium;"><b><u>Method
2 :</u><span style="font-size: medium;">Repetition</span> of 9</b></span></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>Step 1:Count the
digit,Count=N</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>Step 2:First Write N-1
times 9 then 8</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>Step 3 :Again N-1 times 0
then 1</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
Ex:9999^2</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
We See
that there are 4 times 9</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
Now we
write 4-1=3 times 9 then 8</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
9998</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
Now 3
Times 0 then 1</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
0001</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
i.e</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
9999^2=99980001</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm; text-decoration: none;">
<span style="font-size: medium;"><b><u>Method
3 :</u><span style="font-size: medium;">Repetition</span> of 3</b></span></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>Step 1:Count the
digit,Count=N</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>Step 2:First Write N-1
times 1 then 0</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<b>Step 3 :Again N-1 times 8
then 9</b></div>
<div align="LEFT" style="margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
Ex:333333^2</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
We See
that there are 6 times 3</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
Now we
write 6-1=5 times 1 then 0</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
111110</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
Now 5
Times 8 then 9</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
888889</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
i.e</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
333333^2=111110888889</div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div align="LEFT" style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 0cm;">
<br /></div>
</div>
Vimlesh Kumarhttp://www.blogger.com/profile/08177785010966710431noreply@blogger.com0