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    Cube Root of 256

    Cube Root Calculator
    Cube root of

    What is the cube root of 256?

    Answer

    ∛256 =
    4∛4 ≈ 6.3496

    Real cube root: the only number whose cube is 256.

    ≈ — rounded to 4 decimal places. 256 is not the cube of a rational number, so ∛256 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    256 = (2 × 2 × 2) × (2 × 2 × 2) × 2 × 2 = 2⁸
    Take out of the root
    ∛256 = ∛((2³)² × 4) = 2² × ∛4 = 4∛4
    Between cubes
    6³ = 216 < 256 < 343 = 7³, so 6 < ∛256 < 7 and ∛256 ≈ 6.3496

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    https://calculat.io/en/number/cube-root/256Copy
    <a href="https://calculat.io/en/number/cube-root/256">Cube Root of 256 (∛256): Exact Value and Decimal</a>Copy
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    Cube Root of 256 (∛256): Exact Value and Decimal. ∛256 = 4∛4 ≈ 6.3496. 256 = 4³ × 4, so 4 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/256/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    2482∛31 ≈ 6.2828
    2505∛2 ≈ 6.2996
    255≈ 6.3413
    2564∛4 ≈ 6.3496
    257≈ 6.3579
    258≈ 6.3661
    276≈ 6.5108
    Recalculate with different values ↑

    FAQ

    What is the cube root of 256?

    ∛256 = 4∛4 ≈ 6.3496

    How to simplify ∛256?

    Factor 256 into primes: 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛256 = ∛((2³)² × 4) = 4∛4.

    Is ∛256 a rational number?

    No: 256 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 ∛256 is irrational; its decimal never ends and never repeats: ∛256 ≈ 6.3496.

    See Also