Squares, Cubes and Roots
- Qs
- 6
- Marks
- 12
NameDateScore / 12
1.[2]
√36 =
2.[2]
122 =
3.[2]
√4 =
4.[2]
√49 =
5.[2]
√64 =
6.[2]
√144 =
Answer key
- 66 × 6 = 36
- 14412 × 12 = 144
- 22 × 2 = 4
- 77 × 7 = 49
- 88 × 8 = 64
- 1212 × 12 = 144
Squares, Cubes and Roots: Year 8 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 8 (age 13 to 14) 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.
- AC9M8SP01 Investigate and apply Pythagoras' theorem to solve problems involving right-angled triangles.
Sample sheet and answers
Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.