**Square of 2 Digit**__If__

**Method 1:****unit digit is 5**then,

(25)^2

That Means

2 5

**Add 1****2**+

**1**(Add 1 More)=

**3**

**Square of unit Digit**5^2 =

**25**

**Now**2*3=

**6**

(25)^2=625

__Let me explain this trick by taking examples__

**Method 2:**67^2 = [

**6**^2] [

**7**^2]

**+**

**20***

**6***

**7**= 3649+840 = 4489

similarly

25^2 = [2^2][5^2]+20*2*5 = 425+200 = 625

##
__Method
3:__Square of any 2 digit number

- Let me explain this rule by taking
examples

27^2 = (**27+3**)*(**27-3**) +**3^2**= 30*24 + 9 = 720+9 = 729

In this method, we have**to make a number ending with 0**, that's why; we add 3 to 27. -
**1 more example**

78^2 = (78+2)*(78-2) + 2^2 = 80*76 + 4 = 6080+4 = 6084

##
__Method 4:__Square
of any 2 digit number

- The Method is to use (a+b)^2 Formula in
the following Manner
**a^2**/**2ab**/**b^2** - (1)85^2
- 8 5 Break in two part 8 & 5
- 8^2....... 2*8*5......... 5^2 (square of 8
**/**2 * 8 *5**/**square of 5) - 64...............80...............25
- 64..............82................5(Carry 2)
- 72..............2(Carry 8).............5
- 7225
- i.e
**85^2**=**7225**

**Method 5:****Square of numbers near to 50**

Let me explain this rule by taking examples

**(1)37^2 :-**

37 is the near by 50 so, First Calculate 50-37 ,it is 13

**13**is less than 50 ,Therefore

**deduct 13 from 25**i.e.

**25-13(How Much Less)**

25-13=12

13^2=169

Now

12.....

**1**69 (carry 1 )

**37^2=1369**

**(2)57^2 :-**

57 is the near by 50 so, First Calculate 50+7(

**How Much More**).

**7**is greater than 50 therefore

**Add 7 to 25**i.e.

**25+7**

25+7=32

7^2=49

Now

32.....49 (No carry )

**57^2=3249**

**Method 6:****Square of numbers near to 100**

Let me explain this rule by taking examples

**(1)96^2 :-**

First calculate 100-96, it is 4(

**How Much Less**)

**4**is less than 100 ,Therefore

**deduct 4 from 96**i.e.

**96-4=**92

4^2=16

We should written 16 As

**16**

Now

92.....16 (No carry )

**96^2=9216**

(2)

**115^2**

115 is the near by 100 so, First Calculate 100+15(

**How Much More**).

**15**is greater than 100 therefore

**Add 15 to 115**i.e.

**115+15**

115+15=130

15^2=225

Now

130.....

**2**25 (Carry 2)

**115^2=13225**

**Square of Containing Repeated Number**

__Method 1 :__Repetition of 1

Step 1:Count the digit,Count=N

Step 1:Count the digit,Count=N

**Step 2:Now starting From 1 Write The Number till N**

**Step 3 :Now Starting From N Write number till 1**

**Ex: 11111^2**

First
we See that there are 5 times 1

Now we
Write number from 1 to 5

Now
Again From From 5 to 1.

**So Answer is 123454321**

__Method 2 :__Repetition of 9**Step 1:Count the digit,Count=N**

**Step 2:First Write N-1 times 9 then 8**

**Step 3 :Again N-1 times 0 then 1**

Ex:9999^2

We See
that there are 4 times 9

Now we
write 4-1=3 times 9 then 8

9998

Now 3
Times 0 then 1

0001

i.e

9999^2=99980001

__Method 3 :__Repetition of 3**Step 1:Count the digit,Count=N**

**Step 2:First Write N-1 times 1 then 0**

**Step 3 :Again N-1 times 8 then 9**

Ex:333333^2

We See
that there are 6 times 3

Now we
write 6-1=5 times 1 then 0

111110

Now 5
Times 8 then 9

888889

i.e

333333^2=111110888889

## No comments:

## Post a Comment