## Square and Square Root of two digit get using formula1

Square and Square Root get using formula

Formula: (a+b)2 = a2+2ab+b2 i.e, (a / b)2= a2 / 2ab / b2
we applied this formula to obtain the square of a number

### Example 1:

( 57 )2
= ( 5 / 7 )2

Apply formula of a2+2ab+b2
Consider,
572 = ?
A as 5
B as 7 (we break the number in two parts i.e, A as 5 and B as 7 and applied formula )
= 52 / 2 x 5 x 7 / 72
= 25 / 2 x 5 x 7 / 49
a2= 25
b2= 49
2ab = 2 x 5 x 7 = 70
= 25 / 70 / 49
Step 1: Put down 9 carry 4
Step 2: add carry 4 to 70 = 74 put down 4 carry 7
Step 3: add carry 7 to 25 = 32 put down 32
= 3249

All this do on your mind which will help in fast calculation to obtain the answer of Square and Square Root of a number.
we applied this formula to obtain the square of a number

This is similar to the above Example.

### Example 2:

(69)2
= (6/9)2

Consider A as 6, and B as 9.
= 62 / 2 x 6 x 9 / 92
= 36 / 2 x 6 x 9 / 81 (we break the number in two parts i.e, A as 6 and B as 9 and applied formula )
a2 = 36
b2= 81
2ab = 2 x 6 x 9 = 108
=36 / 108 / 81

Step1: put down 1 carry 8
Step2 : add 8 to 108 =116 then put down 6 carry 11
Step3 : and add 11 to 36 = 47 and put down 47