Wednesday, 19 December 2012

Squaring numbers-The better way!!

Calculating the squares of large numbers can be a difficult task but we have found some relations between the numbers that can easily reduce the calculation time and help evaluating the squares

n2 = (n+1) (n-1) +1

i.e  Square of a number= (Preceding number)(Succeeding Number)+1

For e.g.:- n=99
992= (99-1) (99+1) + 1
= 98*100 + 1
= 9801

Hence, now we know that square of 99 = 9801

The other relation is:

n2 = (n-1)2 + (n-1) + n

i.e square of a number= Square of preceding number+Preceding Number+The number itself

For e.g.:- n=13
132 = (13-1)2 + (13-1) +13
= 144 +25
= 169

We can combine the above two identities to form another useful relation

Suppose, we have n=98
We know that 992 = 9801 [i.e. (n+1)2 =9801] from the identity no.1. So, by using the identity no.1 and no.2 we form a relating:-

(n+1)= n2 +n + (n+1)

Hence, we can conclude that,
n2 = (n+1)2 - n – (n+1)

By putting n=98
= (99)2 - 98 - 99
= 9801 - 98 - 99
= 9604