A Trick for finding the Square of a number

Here is a trick which everyone will find greatly useful for finding the square of any given number.

The basic steps are as follows:

1. Assume the number to be X.

2. Find the nearest multiple of 10 from the given number. Let it by Y.

3. Let Z = X - Y

4. Find X + Z

5. Multiply Y with X+Z.

6 Add the square of Z to this product.

You get the desired result.

It appears a bit confusing but can be explained with the following examples:

Eg 1. Let the number be 23 i.e. X=23

Hence Y = 20(Nearest multiple of 10 from 23)

Therefore, Z = X-Y = 23-20 = 3

Now X+Z = 23+3 = 26

Y.(X+Z)= 20(26) = 520

Square of Z = (3 x 3) = 9

Hence Square of 23 = 520 + 9 = 529.

Another example: 

Let the number be 29 i.e. X=29

Hence Y = 30(Nearest multiple of 10 from 29)

Therefore, Z = X-Y = 29-30 = -1

Now X+Z = 29+(-1) = 28

Y.(X+Z)= 30(28) = 840

Square of Z = (-1 x -1) = 1

Hence Square of 29 = 840 + 1 = 841

The trick is very useful and can help you save a lot of time.

However, it requires a good amount of practise. But once perfected it can be a very lethal weapon in your arsenal for belling the CAT.

If any doubts feel free to post your message and i will reply ASAP.