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)
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.
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
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