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    Cube Root of 208

    Cube Root Calculator
    Cube root of

    What is the cube root of 208?

    Answer

    ∛208 =
    2∛26 ≈ 5.925

    Real cube root: the only number whose cube is 208.

    ≈ — rounded to 4 decimal places. 208 is not the cube of a rational number, so ∛208 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    208 = (2 × 2 × 2) × 2 × 13 = 2⁴ × 13
    Take out of the root
    ∛208 = ∛(2³ × 26) = 2∛26
    Between cubes
    5³ = 125 < 208 < 216 = 6³, so 5 < ∛208 < 6 and ∛208 ≈ 5.925

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    https://calculat.io/en/number/cube-root/208Copy
    <a href="https://calculat.io/en/number/cube-root/208">Cube Root of 208 (∛208): Exact Value and Decimal</a>Copy
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    Cube Root of 208 (∛208): Exact Value and Decimal. ∛208 = 2∛26 ≈ 5.925. 208 = 2³ × 26, so 2 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/208/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    2002∛25 ≈ 5.848
    201≈ 5.8578
    207≈ 5.9155
    2082∛26 ≈ 5.925
    213≈ 5.9721
    2166
    217≈ 6.0092
    Recalculate with different values ↑

    FAQ

    What is the cube root of 208?

    ∛208 = 2∛26 ≈ 5.925

    How to simplify ∛208?

    Factor 208 into primes: 208 = 2 × 2 × 2 × 2 × 13. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛208 = ∛(2³ × 26) = 2∛26.

    Is ∛208 a rational number?

    No: 208 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 ∛208 is irrational; its decimal never ends and never repeats: ∛208 ≈ 5.925.

    See Also