Cube Root Calculator
Unlike square roots, cube roots of negative numbers are real: ∛−27 = −3.
Cube root of x
Definition
∛x = y ⇔ y³ = x
Every real number has exactly one real cube root. Because a negative number cubed stays negative, ∛−27 = −3.
Worked example
Simplify ∛54
- Largest perfect cube dividing 54: 27
- ∛54 = ∛(27 × 2) = 3∛2
∛54 = 3∛2 ≈ 3.7798
Where cube roots appear
- Finding the side of a cube from its volume: a 1,000 cm³ cube has sides of ∛1000 = 10 cm.
- Scaling solids: doubling a volume multiplies every length by ∛2 ≈ 1.26.
- Finding the radius of a sphere from its volume.
Perfect cubes
| n | n³ |
|---|---|
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1,000 |