How to Calculate the Cube Root
The cube root of a number is the value that, when multiplied by itself three times, gives the original number. It's the inverse operation of cubing. Cube roots appear in geometry (finding the side of a cube from its volume), physics, and engineering.
The Formula
∛x = x^(1/3)
For a cube with volume V, the side length is:
s = ∛V
Perfect Cube Roots
| Number | Cube Root |
|---|---|
| 1 | 1 |
| 8 | 2 |
| 27 | 3 |
| 64 | 4 |
| 125 | 5 |
| 216 | 6 |
| 343 | 7 |
| 512 | 8 |
| 729 | 9 |
| 1000 | 10 |
Step-by-Step Example
Find ∛512.
Method 1: Recognize 512 = 8³, so ∛512 = 8
Method 2: Use 512^(1/3) on a calculator: 8
Method 3 (estimation): Since 7³ = 343 and 8³ = 512, we know ∛512 is between 7 and 8. Testing 8: 8 × 8 × 8 = 512. ✓
Non-Perfect Cube Roots
For non-perfect cubes, use prime factorization or a calculator.
∛100: Between 4³ = 64 and 5³ = 125, so between 4 and 5. 4.6³ = 97.34, 4.65³ = 100.54, so ∛100 ≈ 4.64
Negative Cube Roots
Unlike square roots, cube roots of negative numbers are real: ∛(−27) = −3 because (−3)³ = −27
Use our cube root calculator for any value.