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: Grade 9 math
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 Grade 9 (age 14 to 15) 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 Common Core State Standards. Check wording and codes against the official document.
- Explain how radical expressions relate to rational exponents using the properties of integer exponents.
Sample sheet and answers
Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.