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.
To build the next square, add one row and one column. A 4 by 4 square needs 4 new dots along one side, 4 along another and 1 in the corner: 16 + 9 = 25. The gaps between square numbers are consecutive odd numbers.
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. It is the smallest positive square number; 0 is also square because 0 × 0 = 0.
What are the square numbers to 100?
The positive square numbers up to and including 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. If your list includes zero, put 0 before 1.
How do you know whether a number is square?
Find a whole number that multiplies by itself to give your number. For 81, 9 × 9 = 81. For 80, 8 × 8 = 64 and 9 × 9 = 81, so 80 falls between two squares and is not square.
Is squaring the same as doubling?
No. Squaring means multiplying a number by itself; doubling means multiplying it by 2. For 6, squaring gives 36 and doubling gives 12. They happen to give the same answer for 2, so use another number when checking the difference.
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
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