What is a square number?
Year 5 recognises square numbers and cube numbers and uses the notation ² and ³. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
A square number is what you get when you multiply a whole number by itself.
What it means
4 × 4 = 16, so 16 is a square number. It is written 4², which is read "4 squared".
They are called square numbers because that many dots can be arranged in a square: 16 dots make a 4 by 4 square.
The square numbers up to 12 × 12 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144.
A worked example
Work out 7²
- The small 2 means multiply 7 by itself.
- 7² = 7 × 7 = 49.
The common mistake
Reading 5² as 5 × 2 = 10. The small 2 means two 5s multiplied together: 5² = 5 × 5 = 25.
How it comes up in the 11+
Which two different square numbers, both smaller than 100, add up to 100?
Answer: 36 and 64
- List the square numbers under 100: 1, 4, 9, 16, 25, 36, 49, 64, 81.
- For each one, check whether 100 minus it is also on the list. 100 − 36 = 64, and 64 is square.
- 36 + 64 = 100, which is 6² + 8² = 10².
Related words and practice
More maths words
Questions parents ask
Is 1 a square number?
Yes. 1 × 1 = 1, so 1 is the first square number.
Why do square numbers have an odd number of factors?
Factors come in pairs, but in a square number one pair uses the same number twice, like 6 × 6 = 36. That number is only counted once, so the total is odd: 36 has 9 factors.
Knowing the words is half of an 11+ maths question
11+ papers use maths vocabulary without explaining it. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.