October 1, 2023

# Squaring of numbers using formulae

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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