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)² = 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