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    Cube Root of 864

    Cube Root Calculator
    Cube root of

    What is the cube root of 864?

    Answer

    ∛864 =
    6∛4 ≈ 9.5244

    Real cube root: the only number whose cube is 864.

    ≈ — rounded to 4 decimal places. 864 is not the cube of a rational number, so ∛864 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    864 = (2 × 2 × 2) × 2 × 2 × (3 × 3 × 3) = 2⁵ × 3³
    Take out of the root
    ∛864 = ∛(2³ × 3³ × 4) = 2 × 3 × ∛4 = 6∛4
    Between cubes
    9³ = 729 < 864 < 1,000 = 10³, so 9 < ∛864 < 10 and ∛864 ≈ 9.5244

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    https://calculat.io/en/number/cube-root/864Copy
    <a href="https://calculat.io/en/number/cube-root/864">Cube Root of 864 (∛864): Exact Value and Decimal</a>Copy
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    Cube Root of 864 (∛864): Exact Value and Decimal. ∛864 = 6∛4 ≈ 9.5244. 864 = 6³ × 4, so 6 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/864/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    7299
    730≈ 9.0041
    7684∛12 ≈ 9.1577
    8646∛4 ≈ 9.5244
    900≈ 9.6549
    925≈ 9.7435
    997≈ 9.99
    Recalculate with different values ↑

    FAQ

    What is the cube root of 864?

    ∛864 = 6∛4 ≈ 9.5244

    How to simplify ∛864?

    Factor 864 into primes: 864 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛864 = ∛(2³ × 3³ × 4) = 6∛4.

    Is ∛864 a rational number?

    No: 864 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 ∛864 is irrational; its decimal never ends and never repeats: ∛864 ≈ 9.5244.

    See Also