# Square numbers – definition, properties and examples

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 n2).

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 n2 is the square number and the square root of n2 should give us back n.

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.
n2 = 32 = 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

02 = 0
12 = 1
22 = 4 = sum of 1 + 3
32 = 9 = sum of 1 + 3 + 5
42 = 16 = sum of 1 + 3 + 5 + 7
52 = 25 = sum of 1 + 3 + 5 + 7 + 9
62 = 36 = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13
72 = 49 = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
82 = 64 = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17
92 = 81 = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
102 = 100 = sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21

### Square numbers 100-400

112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = 400 