You probably already know the shortcut “how to obtain the square of any 2 digit number”. However, if the number is very close to 50. you will see it is much easier and much faster to obtain the squares of such numbers. In this tutorial, you will see how to obtain the square of the number from 41 to 49. A similar shortcut can be used to obtain the squares of the number from 51 to 59.

## Mathematical Proof for squares of the numbers from 41 to 49

Let us understand the algebraic proof behind this shortcut.

Any number from 41 to 49 can be represented as *(50 – a)*. Taking the square of this number we have,

The squares of any 2-digit number from 41 – 49 would be of the form *(25 – a)/a ^{2}* where a is the difference from 50.

Let‘s say, we want to obtain the square of 46.

The complete steps are illustrated in the following figure.

**Step 1:** 46 is 4 less than 50. So *a=4*. Obtain the square of this digit. Obtain the square of 4 to get 16. This forms the RHS part of the answer.

**Step 2:** Subtract 4 from 25 to get 21. This forms the LHS part of the answer.

So, 46^{2}=2116

Let’s consider another example. Can you mentally calculate the square of 49.

The steps are illustrated in the following figure.

Notice 01 in the RHS part of the answer. We need to have 2-digits, so 1^{2} =1 is written as 01 to get the correct answer.

## Try Yourself:

Using this technique, can you obtain the square of:

- 42
- 43
- 47
- 48

If you have any queries regarding this tutorial, please leave a comment. I would be glad to help.