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    Cube Root of 999

    Cube Root Calculator
    Cube root of

    What is the cube root of 999?

    Answer

    ∛999 =
    3∛37 ≈ 9.9967

    Real cube root: the only number whose cube is 999.

    ≈ — rounded to 4 decimal places. 999 is not the cube of a rational number, so ∛999 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    999 = (3 × 3 × 3) × 37 = 3³ × 37
    Take out of the root
    ∛999 = ∛(3³ × 37) = 3∛37
    Between cubes
    9³ = 729 < 999 < 1,000 = 10³, so 9 < ∛999 < 10 and ∛999 ≈ 9.9967

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    https://calculat.io/en/number/cube-root/999Copy
    <a href="https://calculat.io/en/number/cube-root/999">Cube Root of 999 (∛999): Exact Value and Decimal</a>Copy
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    Cube Root of 999 (∛999): Exact Value and Decimal. ∛999 = 3∛37 ≈ 9.9967. 999 = 3³ × 37, so 3 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/999/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    925≈ 9.7435
    997≈ 9.99
    998≈ 9.9933
    9993∛37 ≈ 9.9967
    1,00010
    1,001≈ 10.0033
    1,0248∛2 ≈ 10.0794
    Recalculate with different values ↑

    FAQ

    What is the cube root of 999?

    ∛999 = 3∛37 ≈ 9.9967

    How to simplify ∛999?

    Factor 999 into primes: 999 = 3 × 3 × 3 × 37. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛999 = ∛(3³ × 37) = 3∛37.

    Is ∛999 a rational number?

    No: 999 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 ∛999 is irrational; its decimal never ends and never repeats: ∛999 ≈ 9.9967.

    See Also