What is a square number?

A square number is an integer that is a perfect square of another integer.

In plain English, if you multiply a whole number by itself, the result is a square number, for example 5 x 5 = 25, so 25 is a square number.

Square numbers are very useful, and they often come up in exam questions. If you can remember the first 15 square numbers, or at least learn to recognise them, it can save you a lot of thinking time in exams.

Square Numbers

1 x   1 =     1

2 x   2 =     4

3 x   3 =     9

4 x   4 =   16

5 x   5 =   25

6 x   6 =   36

7 x   7 =   49

8 x   8 =   64

9 x   9 =   81

10 x 10 = 100

11 x 11 = 121

12 x 12 = 144

13 x 13 = 169

14 x 14 = 196

15 x 15 = 225

What is a square root?

A square root is a number or quantity that when multiplied by itself is equal to a given number or quantity. For example, the square root of 144 is 12 because 12 x 12 = 144.

A square root does not have to be a whole number or integer. For example the square root of 10 is 3.16227766 because  3.16227766 x 3.16227766 = 10

 Square number Square root 1 1 4 2 9 3 16 4 25 5 36 6 49 7 64 8 81 9 100 10 121 11 144 12 169 13 196 14 225 15