The cube root of n is the number that, when cubed, gives n back.
About this calculator
The cube root of n is the number that, when cubed, gives n back. ∛27 = 3 because 3 × 3 × 3 = 27. Unlike square roots, cube roots work on negative numbers: ∛(−8) = −2.
Perfect cubes to remember: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000. Volume problems often need cube roots — if a box holds 27 cubic metres with equal edges, each edge is ∛27 = 3 metres.
Reverse with the [[cube]] calculator. For general nth roots try [[root]]. For volume of a cube from edge length use [[cube]] and geometry volume tools.
Common uses
- Find edge length from cube volume
- Evaluate ∛27 or other perfect cubes
- Handle negative radicands in algebra class
- Check cube-root estimates for engineering sketches
- Verify volume-to-dimension conversions
Frequently asked questions
What is the cube root of 27?
∛27 = 3 because 3³ = 3 × 3 × 3 = 27. It is a perfect cube with an exact integer root.
Can cube roots be negative?
Yes. ∛(−8) = −2 because (−2) × (−2) × (−2) = −8. Odd roots preserve the sign of the input.
How is cube root different from square root?
Square root requires n ≥ 0 for real answers. Cube root accepts any real n. ∛n equals n^(1/3).
What is ∛1000?
∛1000 = 10 exactly. Ten cubed is 1000 — useful for converting between cubic centimetres and litres in rough estimates.