11+ Maths · Topic explained
Square and cube numbers
Why is 9 called a square number? Can you picture it?
The big idea
A square number is a number times itself; a cube number is a number times itself, three times.
Picture it
Build squares of tiles: 1, 4, 9, 16. The number of tiles in each square is a square number.
Key words
- square number
- A number times itself: 1, 4, 9, 16, 25, 36…
- squared (²)
- Times itself: 5² = 5 × 5 = 25.
- cube number
- A number times itself three times: 1, 8, 27, 64, 125…
- cubed (³)
- 2³ = 2 × 2 × 2 = 8.
Worked examples
- 1Warm-up
What is 4²?
- 4² means 4 × 4
- 4² = 16
- 211+ standard
Work out 2³ + 3²
- 2³ = 2 × 2 × 2 = 8
- 3² = 3 × 3 = 9
- 8 + 9 = 17
- 311+ standard
Which number between 50 and 70 is a square number?
- 7² = 49 (too small)
- 8² = 64
- 9² = 81 (too big)
- 411+ standard
A square has an area of 81 cm². How long is each side?
- Which number times itself is 81?
- 9 × 9 = 81, so each side is 9 cm
The common mistake
The mistake
5² = 10, because it's 5 × 2.
Instead
5² = 5 × 5 = 25.
Why: The small 2 says how many fives to multiply together, not what to multiply by.
Where it comes up in the 11+
Spotting square and cube numbers in lists, powers inside calculations, and square areas.
The video
Video coming soon
We're making a short video that explains square and cube numbers step by step. Until then, everything it covers is on this page.
Free printable
Square and cube numbers worksheet
Practice questions on this topic to print and try on paper, at home or on the way to school.
Download the worksheet (PDF)Free account needed: it takes a minute.
Quick quiz
Have a go first, then tap to see the answer.
1. What is 7²?
- 14
- 49
- 77
- 343
Show the answerHide the answer
49
7 × 7 = 49.
2. What is 3³?
- 9
- 27
- 33
- 81
Show the answerHide the answer
27
3 × 3 × 3 = 27.
3. Which number is both a square number and a cube number: 16, 27, 64 or 100?
- 16
- 27
- 64
- 100
Show the answerHide the answer
64
64 = 8 × 8 and 64 = 4 × 4 × 4.