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    Cube Root of 1/3

    Cube Root Calculator
    Cube root of

    What is the cube root of 1/3?

    Answer

    ∛(1/3) =
    ∛9/3 ≈ 0.6934

    Real cube root: the only number whose cube is 1/3.

    ≈ — rounded to 4 decimal places. 1/3 is not the cube of a rational number, so ∛(1/3) is irrational: its decimal expansion never ends and never repeats.

    Root of a fraction
    ∛(1/3) = ∛1/∛3 = 1/∛3
    Multiply by ∛(3²) = ∛9
    1/∛3 = ∛9/∛27 = ∛9/3 ≈ 0.6934

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    https://calculat.io/en/number/cube-root/1-3Copy
    <a href="https://calculat.io/en/number/cube-root/1-3">Cube Root of 1/3 (∛(1/3)): Exact Value and Decimal</a>Copy
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    Cube Root of 1/3 (∛(1/3)): Exact Value and Decimal. ∛(1/3) = ∛9/3 ≈ 0.6934. ∛(1/3) = ∛1/∛3; multiplying by ∛9 clears the root from the denominator.
    https://calculat.io/en/number/cube-root/1-3/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    1/4∛2/2 ≈ 0.63
    8/272/3 ≈ 0.6667
    0.3≈ 0.6694
    1/3∛9/3 ≈ 0.6934
    0.3430.7
    343/10007/10 = 0.7
    0.36≈ 0.7114
    Recalculate with different values ↑

    FAQ

    What is the cube root of 1/3?

    ∛(1/3) = ∛9/3 ≈ 0.6934

    Why is ∛(1/3) = ∛9/3?

    ∛(1/3) = ∛1/∛3. Multiplying the numerator and the denominator by ∛(3²) = ∛9 makes the denominator a perfect cube: ∛9/∛27 = ∛9/3. The value does not change; only the root leaves the denominator.

    Is ∛(1/3) a rational number?

    No: 1/3 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 ∛(1/3) is irrational; its decimal never ends and never repeats: ∛(1/3) ≈ 0.6934.

    See Also