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    Cube Root of −64

    Cube Root Calculator
    Cube root of

    What is the cube root of −64?

    Answer

    ∛(−64) =
    −4

    Real cube root: the only number whose cube is −64.

    A negative number has a negative cube root: (−4)³ = −64. There is no real square root of −64.

    Sign
    ∛(−64) = −∛64, because (−a)³ = −a³
    Prime factors
    64 = (2 × 2 × 2) × (2 × 2 × 2) = 2⁶
    Take out of the root
    ∛64 = ∛((2³)²) = 2² = 4
    Check
    4 × 4 × 4 = 64 ✓

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    https://calculat.io/en/number/cube-root/-64Copy
    <a href="https://calculat.io/en/number/cube-root/-64">Cube Root of −64 (∛(−64)): Exact Value and Decimal</a>Copy
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    Cube Root of −64 (∛(−64)): Exact Value and Decimal. ∛(−64) = −4. 64 = 4³: 4 × 4 × 4 = 64. The minus comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/-64/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −125−5
    −108−3∛4 ≈ −4.7622
    −81−3∛3 ≈ −4.3267
    −64−4
    −54−3∛2 ≈ −3.7798
    −49−∛49 ≈ −3.6593
    −32−2∛4 ≈ −3.1748
    Recalculate with different values ↑

    FAQ

    What is the cube root of −64?

    ∛(−64) = −4

    Why does the cube root of −64 exist but the square root does not?

    A cube keeps the sign: (−4)³ = −64, so ∛(−64) = −4. The square of any real number is never negative, so no real number squared gives −64.

    Is ∛(−64) a rational number?

    Yes: ∛(−64) = −4, a whole number.

    See Also