Cube Root Calculator
Compute cube roots, cubes, and general nth roots with exact radical forms, decimal approximations, and a nearby perfect-cubes number line.
Cube root
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Number (x) ?
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Root degree (n) ?
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Formula
=
x1/3
Cube root: ∛x = x1/3
Simplification: ∛(a³ × b) = a∛b
Product rule: ∛(a × b) = ∛a × ∛b
Quotient rule: ∛(a ÷ b) = ∛a ÷ ∛b (b ≠ 0)
Negative input: ∛(−x) = −∛x (real, not imaginary)
Nth root: n√x = x1/n
- ∛x
- The real number that when cubed gives x.
- Perfect cube
- A number whose cube root is an integer (1, 8, 27, 64, 125, 216, …).
- Simplified radical
- Factor out the largest perfect cube from under the radical sign, e.g. ∛24 = ∛(8·3) = 2∛3.
- Negative radicand
- Unlike square roots, cube roots of negatives are real. ∛(−27) = −3 because (−3)³ = −27.
Worked example — your number
- Radicand: —
- Largest perfect-cube factor: —
- Factor: —
- Pull out the cube: —
- Exact: —
- Decimal: —
Every real number has exactly one real cube root. Cube roots preserve sign: positive in → positive out, negative in → negative out. By convention ∛x refers to the principal (real) root — the complex roots are used only in higher algebra.