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

**Square and Square Root get using formula
**

Formula:** (a+b) ^{2} = a^{2}+2ab+b^{2} i.e, (a / b)^{2}= a^{2} / 2ab / b^{2}**

we applied this formula to obtain the square of a number

**Example 1:**

**( 57 ) ^{2}**

= ( 5 / 7 )

^{2}

**Answer :**

Apply formula of** a ^{2}+2ab+b^{2}**

Consider,

57

^{2}= ?

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 )

= 5

^{2}/ 2 x 5 x 7 / 7

^{2}

= 25 / 2 x 5 x 7 / 49

a

^{2}= 25

b

^{2}= 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

and answer is

**3249,**

**= 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}

**Answer :**

Consider **A as 6, and B as 9.**

= 6^{2} / 2 x 6 x 9 / 9^{2}

= 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** )

a^{2} = 36

b^{2}= 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**

S**tep3 :** and add 11 to 36 = 47 and** put down 47**

=** so answer is 4761,**

=** 4761**

**Note: All this do on your mind which will help in fast calculation to obtain the answer of Square and Square Root of a number.**