A square number is a result of multiplying a **whole** number with itself. In other words, when we take a number and multiply that number with itself then the result that we get is called a **square number** or a **perfect square**.

For example, if we take 2 and then multiply 2 x 2 we get 4. We will then call the result 4 as the square number because it is the result of squaring the number or multiplying the same number with itself.

*Multiplying a number with itself is called squaring the number (denoted by n ^{2}).*

100 is a square number because it is a product of 10 x 10.

** Technical definition**: The product of an integer with itself results in another integer that is called a square number.

(If it is too confusing to remember the technical definition then don’t worry about it because we are interested in understanding the concept and not learn by rote.)

## What are the properties of a square number?

The square numbers are **whole numbers** that are **non-negative** integers and whose square root will result in an **integer**.

If **n** is an integer the **n ^{2}** is the square number and the square root of

**n**should give us back n.

^{2}** Interesting fact**: The square number for n is equal to the

**sum**of the first n odd numbers in the sequence.

*For example, *

If n = 3, then the sum of first 3 odd numbers 1 + 3 + 5 is equal to 9.

n^{2} = 3^{2} = 9

## Examples of square numbers

The square numbers from 1 to 100 are: **1, 4, 9, 25, 36, 49, 64, 81, 100**

The even square numbers from 1 to 100 are: **4, 36, 64, 100**

The odd square numbers from 1 to 100 are: **1, 9, 25, 49, 81**

### Square numbers 0-100

0^{2} = **0**

1^{2} = **1**

2^{2} = **4** = sum of 1 + 3

3^{2} = **9** = sum of 1 + 3 + 5

4^{2} = **16** = sum of 1 + 3 + 5 + 7

5^{2} = **25** = sum of 1 + 3 + 5 + 7 + 9

6^{2} = **36** = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13

7^{2} = **49** = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

8^{2} = **64** = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17

9^{2} = **81** = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

10^{2} = **100** = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21

### Square numbers 100-400

11^{2} = **121**

12^{2} = **144**

13^{2} = **169**

14^{2} = **196**

15^{2} = **225**

16^{2} = **256**

17^{2} = **289**

18^{2} = **324**

19^{2} = **361**

20^{2} = **400**

## Square Number Worksheet – free download

### Download the square numbers worksheet

Practice this worksheet to get clarity on the concept.

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