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    Cube Root of −54

    Cube Root Calculator
    Cube root of

    What is the cube root of −54?

    Answer

    ∛(−54) =
    −3∛2 ≈ −3.7798

    Real cube root: the only number whose cube is −54.

    ≈ — rounded to 4 decimal places. −54 is not the cube of a rational number, so ∛(−54) is irrational: its decimal expansion never ends and never repeats.

    A negative number has a negative cube root: (−3∛2)³ = −54. There is no real square root of −54.

    Sign
    ∛(−54) = −∛54, because (−a)³ = −a³
    Prime factors
    54 = 2 × (3 × 3 × 3) = 2 × 3³
    Take out of the root
    ∛54 = ∛(3³ × 2) = 3∛2
    Between cubes
    3³ = 27 < 54 < 64 = 4³, so 3 < ∛54 < 4 and ∛54 ≈ 3.7798

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    https://calculat.io/en/number/cube-root/-54Copy
    <a href="https://calculat.io/en/number/cube-root/-54">Cube Root of −54 (∛(−54)): Exact Value and Decimal</a>Copy
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    Cube Root of −54 (∛(−54)): Exact Value and Decimal. ∛(−54) = −3∛2 ≈ −3.7798. 54 = 3³ × 2, so 3 comes out of the root. The minus comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/-54/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −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
    −27−3
    Recalculate with different values ↑

    FAQ

    What is the cube root of −54?

    ∛(−54) = −3∛2 ≈ −3.7798

    Why does the cube root of −54 exist but the square root does not?

    A cube keeps the sign: (−3∛2)³ = −54, so ∛(−54) = −3∛2. The square of any real number is never negative, so no real number squared gives −54.

    Is ∛(−54) a rational number?

    No: −54 is not the cube of a rational number, and the cube root of a fraction p/q in lowest terms is rational only when p and q are both cubes. So ∛(−54) is irrational; its decimal never ends and never repeats: ∛(−54) ≈ −3.7798.

    See Also