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    Cube Root of −1

    Cube Root Calculator
    Cube root of

    What is the cube root of −1?

    Answer

    ∛(−1) =
    −1

    Real cube root: the only number whose cube is −1.

    A negative number has a negative cube root: (−1)³ = −1. There is no real square root of −1.

    Sign
    ∛(−1) = −∛1, because (−a)³ = −a³
    Check
    1 × 1 × 1 = 1 ✓

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    https://calculat.io/en/number/cube-root/-1Copy
    <a href="https://calculat.io/en/number/cube-root/-1">Cube Root of −1 (∛(−1)): Exact Value and Decimal</a>Copy
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    Cube Root of −1 (∛(−1)): Exact Value and Decimal. ∛(−1) = −1. (−1) × (−1) × (−1) = −1: the only real number whose cube is −1. The minus comes out of the root.
    https://calculat.io/en/number/cube-root/-1/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −5−∛5 ≈ −1.71
    −3−∛3 ≈ −1.4422
    −2−∛2 ≈ −1.2599
    −1−1
    −0.5≈ −0.7937
    −1/2−∛4/2 ≈ −0.7937
    −1/8−1/2 = −0.5
    Recalculate with different values ↑

    FAQ

    What is the cube root of −1?

    ∛(−1) = −1

    Why does the cube root of −1 exist but the square root does not?

    A cube keeps the sign: (−1)³ = −1, so ∛(−1) = −1. The square of any real number is never negative, so no real number squared gives −1.

    Is ∛(−1) a rational number?

    Yes: ∛(−1) = −1, a whole number.

    See Also