Cube Root Calculator (∛n)
∛n with perfect-cube detection, simplified surd form, and decimal expansion.
Result
∛n
4.000000
Perfect cube: ∛64 = 4.
- n64
- Decimal4.0000000000
- Perfect cube?Yes
- Simplified surd4
- n³262,144.000000
Step-by-step
- Decimal: ∛64 = 4.00000000.
- 64 is a perfect cube.
How to use this calculator
- Enter any real number (positive or negative).
- Read decimal + simplified surd.
About this calculator
The cube root of n is the value x where x³ = n. Unlike square roots, cube roots accept negative inputs (∛(−8) = −2). Perfect cubes: 1, 8, 27, 64, 125, …. Simplified surd: ∛54 = ∛(27 × 2) = 3∛2. JavaScript provides Math.cbrt which handles negatives correctly and runs fast on hardware. Useful in geometry (volume of a cube of size x = x³), finance (annualized growth from a 3-period total), and music (frequency ratios).
Frequently asked
Odd functions: y = x³ is one-to-one over all reals. (−2)³ = −8, so ∛(−8) = −2. Square root only defined for non-negatives in real domain.
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