Finding the square of a number between 25 to 75

The earlier trick for finding the square was a more generic one and can be implemented to find out the square of any number. You can find the trick here:

http://conceptsforcat.blogspot.com/2009/03/trick-for-squares-of-number.html

However, at points it is time consuming and needs good multiplication skills.

This trick is a more specific one to find out the square of any number between 25 and 75.

The only pre-requisites for this trick is the knowledge of the squares of 1 to 25.

So it goes this way:

1. Assume the number to be X.

2. Let the difference of the number from 25 be Y i.e. Y = (X - 25)

3. Let the difference of the number from 50 be Z i.e. Z = (X - 50)

4. The square of the number will be [(100 x Y) + (Square of Z)].

The above trick can be explained from the following examples:

Eg1. Let the number be 33 i.e. X = 33

Hence, Y = (X - 25) = (33 - 25) = 8

Also,     Z = (X - 50) = (33 -50) = - 17

Therefore the square of X = [(100Y) + (Square of Z)]

                                              = [(100 x 8) + (-17 x -17)]

                                              = 800 + 289

                                             = 1089.

i.e. Square of 33 = 1089.

Eg2. Let the number be 53 i.e. X = 53

Hence, Y = (X - 25) = (53 - 25) = 28

Also,     Z = (X - 50) = (53 -50) = 3

Therefore the square of X = [(100Y) + (Square of Z)]

                                              = [(100 x 28) + (3 x 3)]

                                              = 2800 + 9

                                             = 2809.

i.e. Square of 53 = 2809.

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.