Finding the Square of a Number

Table of Contents

• Finding the Square of a Number
• What’s Next?

In the previous segment, we learnt what a Square of a number is. In this segment, we will learn how to find the square of a number.

How to find the square of a number?

It is easy to find the square of small numbers. For example,

2² = 2 × 2 = 4

5² = 5 × 5 = 25

9² = 9 × 9 = 81

Let us understand how to find the square of larger numbers with a few examples. Square of 23

To find the square of 23, without multiplying 23 with 23, we can use the following method:

23 = 20 + 3

This means,

23² = (20 + 3)²

= (20 + 3)(20 + 3)²

= 20(20 + 3) + 3(20 + 3)

= (20 × 20) + (20 × 3) + (3 × 20) + (3 × 3)

= 400 + 60 + 60 + 9

= 529

This method can be used to find the square of any two-digit number.

But for two-digit numbers ending with 5, there is a simpler method to find the square. For a two-digit number ‘a5’; the square of ‘a5’ is given by [? × (? + 1) × 100] + 25.

Let us understand this by finding the square of 25.

25² = [2 × (2 + 1) × 100] + 25

= (2 × 3 × 100) + 25