SQUARE

                        Square of 2 Digit

Method 1:If 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

Method 2:Let me explain this trick by taking examples
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.....169 (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.....225 (Carry 2)

115^2=13225

           Square of Containing Repeated Number

Method 1 :Repetition of 1

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