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    Cube Root of 108

    Cube Root Calculator
    Cube root of

    What is the cube root of 108?

    Answer

    ∛108 =
    3∛4 ≈ 4.7622

    Real cube root: the only number whose cube is 108.

    ≈ — rounded to 4 decimal places. 108 is not the cube of a rational number, so ∛108 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    108 = 2 × 2 × (3 × 3 × 3) = 2² × 3³
    Take out of the root
    ∛108 = ∛(3³ × 4) = 3∛4
    Between cubes
    4³ = 64 < 108 < 125 = 5³, so 4 < ∛108 < 5 and ∛108 ≈ 4.7622

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    https://calculat.io/en/number/cube-root/108Copy
    <a href="https://calculat.io/en/number/cube-root/108">Cube Root of 108 (∛108): Exact Value and Decimal</a>Copy
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    Cube Root of 108 (∛108): Exact Value and Decimal. ∛108 = 3∛4 ≈ 4.7622. 108 = 3³ × 4, so 3 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/108/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    102≈ 4.6723
    103≈ 4.6875
    107≈ 4.7475
    1083∛4 ≈ 4.7622
    110≈ 4.7914
    110.5924.8
    111≈ 4.8059
    Recalculate with different values ↑

    FAQ

    What is the cube root of 108?

    ∛108 = 3∛4 ≈ 4.7622

    How to simplify ∛108?

    Factor 108 into primes: 108 = 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: ∛108 = ∛(3³ × 4) = 3∛4.

    Is ∛108 a rational number?

    No: 108 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 ∛108 is irrational; its decimal never ends and never repeats: ∛108 ≈ 4.7622.

    See Also