What are square numbers?

Square numbers
We explain what square numbers are and how children are taught to know square numbers plus the corresponding squares of multiples of 10. We also explain how knowledge of square numbers can help when it comes to working out the area of a square.

What are square numbers?

When you multiply a number by itself, the result is a square number:

1 x 1 = 1                           7 x 7 = 49
2 x 2 = 4                           8 x 8 = 64
3 x 3 = 9                           9 x 9 = 81
4 x 4 = 16                        10 x 10 = 100
5 x 5 = 25                        11 x 11 = 121
6 x 6 = 36                        12 x 12 = 144

and so on.

To write the mathematical formula for square numbers we add a small 2 next to and above the number, for example: 32.

Square numbers in Key Stage 2

Children in Years 5 and 6 are expected to know all the above square numbers, plus the corresponding squares of multiples of 10 (20 x 20 = 400, 30 x 30 = 900, 40 x 40 = 1600, etc.).

Knowledge of square numbers can help children when it comes to working out the area of a square. For example: they may be shown a square (not drawn to scale) and told the area of the square is 81cm². If they are asked to work out the length of each side, their knowledge of square numbers will mean they will know instantly that each side of the square is 9cm.

Children in Year 6 will need to solve puzzles and investigations involving square numbers. Here are some examples:

Karen has these number cards:

If she puts all the cards in a hat and picks one out at random, what is the probability she will pick a square number?

Answer: since there are 3 square numbers: 49, 100 and 16, the probability she will pick a square number is 3/8.

Another investigation example:

Two square numbers are added together to make another square number. What are they?

One possible answer is 16 + 9 which equals 25. 

Children in upper KS2 (but more usually KS3) will also learn about cube numbers.