Square of a number

Square of a number  by using base method:

I mentioned base method in two digit multiplication. So I will start with an example.

Ex 1 : 13 x 13

10 is the nearest round figure value. So 10 is base

13 = 10 + 3

13 ₊₃ x 13 ₊₃ = 13 +3 / 3 x3 = 16 / 9 = 169

Steps :

1. Find nearest round figure value

2. Follow base multiplication method

Ex 2: 14 x 14 = ?

14 x 14 = 14+4 / 4x4 = 18 / 16 = 196

Ex 3 : 23 x 23 = ?

Here base is 20

23 x 23 = 23+3 / 3x3 = 26 / 9

When base is 20, need to multiply 10's digit with 2

when base is 30, need to multiply 10's digit with 3

when base is 40, need to multiply 10's digit with 4

So

result = 26 x 2 / 9 = 52 / 9 = 529

Ex 4 : 44 x 44 = ?

Base = 40

result = 44 + 4 / 4x4 = 48 / 16 = 48 / 16
         = 48 x 4 /16 ( As base is 40 )
         = 192 / 16 ( 1 carry forward )
         = 1936

Try 56², 73² and 82²