Square and Cube Roots — Free KS3 Worksheet
A free, printable KS3 worksheet on square and cube roots, with a full worked answer key. 15 questions graded easy to hard for Years 7, 8 and 9, building from square roots and cube roots up to estimating a root that isn't exact, and worded garden and box problems.
A root runs a power backwards. The square root of 49 asks what number multiplied by itself gives 49, and the cube root of 125 asks what number multiplied by itself three times gives 125. If the squares and cubes are solid, roots are mostly a matter of reading the question in that direction.
What is on the sheet
Square roots first, all of them exact, so the focus stays on the reversal. Cube roots next, where the numbers are larger and the answers are smaller, which surprises people the first time. Then mixed calculations with roots inside them. The last group asks for an estimate of a root that is not exact, by finding the two whole numbers it sits between, which is the skill that actually gets used when the calculator is away.
Marking it
The square and cube roots lesson works forwards and backwards on the same numbers, which is what makes the reversal stick.
Keep going
More number properties practice
Prime Numbers — Free KS3 Worksheet
A free, printable KS3 worksheet on prime numbers, with a full worked answer key. 15 questions graded easy to hard for Years 7, 8 and 9, building from spotting small primes up to working out how far you actually have to test.
Factors and Multiples — Free KS3 Worksheet
A free, printable KS3 worksheet on factors and multiples, with a full worked answer key. 15 questions graded easy to hard for Years 7, 8 and 9, building from listing factors and multiples up to knowing exactly where to stop.
Square and Cube Numbers — Free KS3 Worksheet
A free, printable KS3 worksheet on square and cube numbers, with a full worked answer key. 16 questions graded easy to hard for Years 7, 8 and 9, building from squares and cubes up to higher powers, mixed calculations and worded patio and box problems.
Want all 8 number properties worksheets at once?
One PDF, 125 questions, every answer key included, in teaching order. Every sheet in it is free on its own page too. The pack just saves you collecting them one at a time.