# Squaring Numbers Near 50

Squaring a number that ends in 50 is very easy.

This method can be applied to any number which is on either direction of 50, i.e. 55, 52, 47, …., 59 and so on.

There can be two cases:

• Case 1: For numbers greater than 50

The result is comprised of two “parts”

The “right part” is always the right digit squared

The “left part” is the left digit squared plus the right digit.

Let’s explore this with an example:

542

Here, the left digit is 5 and the right digit is 4.

So, the right part of the answer is square of the right digit, i.e. 42 = 16.

And, left part of the answer is square of left digit + right digit, i.e. 52+4 = 29

542 52+4 / 42 29 / 16 → 2916

Another example, 532 25+3 / 9 28 / 9 → 2809

• Case 2: For numbers less than 50

The result is comprised of two “parts”

The “right part” is always the bar of the right digit squared

The “left part” is the square of 5 minus the bar of the right digit

Let’s explore this with an example:

482

48 is near 50. The left digit is 4 and the right digit is 8.

So, the right part of the answer is the square of “bar of 8”.

Bar of 8 is 2.

Square of 2 is 22 = 4.

And, left part of the answer is square of 5, i.e. 52-2 = 23.

482 52-2 / (bar 8)2 25-2 / 22 23 / 04 → 2304

Another example, 462 25-4 / 42 21 / 16 → 2116