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.
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.
Example : find the square of 1009.
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.
( 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
Example 2. Find the square of 507.
Let b=7 . Then
= 514 x 500+ 49
Thus we see that the above formulae can help us to find the squares of any number above and below a round figure respectively.