Squares, Cubes and Roots
- Qs
- 6
- Marks
- 18
NameDateScore / 18
1.[3]
√81 =
2.[3]
202 =
3.[3]
√9 =
4.[3]
√121 =
5.[3]
√144 =
6.[3]
√400 =
Answer key
- 99 × 9 = 81
- 40020 × 20 = 400
- 33 × 3 = 9
- 1111 × 11 = 121
- 1212 × 12 = 144
- 2020 × 20 = 400
Squares, Cubes and Roots: Year 10 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 10 (age 15 to 16) as a topic to introduce. 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 Australian Curriculum v9. Check wording and codes against the official document.
- AC9M10N01 Evaluate and simplify numerical expressions using index laws including negative and fractional powers.
Sample sheet and answers
Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.