Perfect Cube Calculator
The perfect cube calculator helps you identify if a given number is a perfect cube or not.
Perfect square?Yes, 27²nearest square root is 27
Perfect cube?Yes, 9³
All perfect powers27^2, 9^3, 3^6
Prime factorisation3^6
Every root up to 12
| Index | Root | Exact? |
|---|---|---|
| 2 | 27 | Yes — 27^2 |
| 3 | 9 | Yes — 9^3 |
| 4 | 5.19615242 | No |
| 5 | 3.73719282 | No |
| 6 | 3 | Yes — 3^6 |
| 7 | 2.5642542 | No |
| 8 | 2.27950706 | No |
| 9 | 2.08008382 | No |
| 10 | 1.93318204 | No |
| 11 | 1.8207401 | No |
| 12 | 1.73205081 | No |
The method
test whether n is a perfect square, cube or higher power
Reading it off the factorisation
A number is a perfect kth power exactly when every exponent in its prime factorisation is divisible by k. 729 = 3⁶, and 6 divides by both 2 and 3, so it is both a perfect square (27²) and a perfect cube (9³) — and indeed a perfect sixth power (3⁶).