To find square of a number close to ‘100’

Using this trick you can find the square of a number which is near 100.

Short trick used: Let the number whose square is to be found be ‘A’. and let ‘D’ be the difference of the number from 100,

then square can be found using following formula:

(A)2 = (A – D) | (D)2….(if A is smaller than 100)

or 

(A)2 = (A + D) | (D)2….(if A is greater than 100)

 

Example:

find the square of 96.

Solution:

Here A = 96 and D = 100 – 96  = 4

(96)2 = (A – D) | (D)2    (As 96 is smaller than 100)
= 96 – 4 | (4)2
= 92 | 16
= 9216

 

Note: Right part of our answers should consist of 2 digits. if it is more than 2 digits then carry forward the extra digits to the left part. and if it is less than 2 digits than add ’0’ before the number  to make it 2 digit number.

Let me clarify this with the help of an example.

 

Example:

Find the square of 98.

Solution:

Here A = 98. D = 100 – 98  = 2

Now,

(98)2 = (A – D) | (D)2    (As 98 is smaller than 100)
= 98 – 2 | (2)2
= 96 | 4    (since 4 is single digit number. we will add a ’0’ before it to make it 2 digit number)
= 96 | 04
= 9604

 

Example:

Let’s find the square of 103.

Solution:

Here A = 103. D = 103 – 100  = 3

(103)2 = (A + D) | (D)2   (As 103 is greater than 100)
= 103 + 3 | (3)2
= 106 | 9      (since 9 is single digit number. we will add a ’0’ before it to make it 2 digit number)
= 106 | 09
= 10609