Squares, Cubes and Roots
- Qs
- 6
- Marks
- 6
NameDateScore / 6
1.[1]
√9 =
2.[1]
52 =
3.[1]
√4 =
4.[1]
√9 =
5.[1]
√16 =
6.[1]
√25 =
Answer key
- 33 × 3 = 9
- 255 × 5 = 25
- 22 × 2 = 4
- 33 × 3 = 9
- 44 × 4 = 16
- 55 × 5 = 25
Squares, Cubes and Roots: Year 7 maths
This topic covers calculating squares, cubes, and their corresponding roots. The worksheet reinforces mental recall of common values and estimation of non-perfect roots.
What this covers
Squares, Cubes and Roots is taught in Year 7 (age 11 to 12, KS3) as a main teaching focus. It sits in the Number strand.
Worked example
Calculate 5^2 + sqrt(64).
- Evaluate the square: 5^2 = 25
- Evaluate the square root: sqrt(64) = 8
- Add the results: 25 + 8 = 33
Answer: 33
Difficulty scale
The sheet generator offers five difficulty settings for this topic.
- Squares of integers from 1 to 12
- Square roots of perfect squares up to 144 and cubes from 1 to 5
- Cube roots up to 125 and mixed order-of-operations with roots
- Higher squares up to 20^2, cubes up to 10^3, and fractional roots like sqrt(14)
- Estimating non-perfect square roots between consecutive integers
Common mistakes
- Multiplying the base by 2 instead of squaring it (e.g. 5^2 = 10)
- Halving a number instead of finding its square root (e.g. sqrt(36) = 18)
Curriculum links
Indicative matches to National Curriculum for England. Check wording and codes against the official document.
- Use integer powers and associated real roots, recognising powers of 2, 3, 4, 5 and square and cube roots.
Sample sheet and answers
Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.