Squaring of numbers means multiplying a number by itself. There are various formulae used in general mathematics to square numbers instantly. Let us discuss them one by one.

**(i) **

This formula is generally use to square those numbers which are near multiples of 10. For example , suppose we have to find the square of 2011. We represent the number 2011 as 2000+11. Thus we have converted it into a form of (a+b) where the value of a is 2000 and the value of b is 11.

Now

=4044121

Example : find the square of 1009.

Sol.

= 1000000+18000+81

=1018081

**(ii)**

This formula is very much like the first one. The only difference is that the middle term contain negaive sign.

Example : Find the square of 792.

Sol.

=640000- 12800+64

=6 27264.

**(iii) **

**( How it comes! **We know that . Therefore )

Suppose we are asked to find the square of a number. Let’s call this number ‘a’. Now in this case we will find another number ‘b’ in such a way that the product (a+b)(a-b) and the square of ‘b’ can be easily find.

Example 1. Find the square of 66.

Sol. In this case, the value of ‘a’ is 64. Now, we know that

** **

substituting the value of ‘a’ as 64 , we get

Now , we have to substitute the value of ‘b’ with such a number that the whole equation becomes easy to solve. Let us suppose the value of b= 4.

Then the equation becomes

=68 x 60 +16

= 4080+16

= 4096

Example 2. Find the square of 507.

Let b=7 . Then

= 514 x 500+ 49

= 257000+49

= 257049

Thus we see that the above formulae can help us to find the squares of any number above and below a round figure respectively.

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