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    Cube Root of 1/4

    Cube Root Calculator
    Cube root of

    What is the cube root of 1/4?

    Answer

    ∛(1/4) =
    ∛2/2 ≈ 0.63

    Real cube root: the only number whose cube is 1/4.

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

    1/4 = 0.25.

    Root of a fraction
    ∛(1/4) = ∛1/∛4 = 1/∛4
    Multiply by ∛(4²) = ∛16
    1/∛4 = ∛16/∛64 = ∛16/4
    Take out of the root
    ∛16/4 = ∛(2³ × 2)/4 = 2∛2/4 = ∛2/2 ≈ 0.63

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    https://calculat.io/en/number/cube-root/1-4Copy
    <a href="https://calculat.io/en/number/cube-root/1-4">Cube Root of 1/4 (∛(1/4)): Exact Value and Decimal</a>Copy
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    Cube Root of 1/4 (∛(1/4)): Exact Value and Decimal. ∛(1/4) = ∛2/2 ≈ 0.63. ∛(1/4) = ∛1/∛4; multiplying by ∛16 clears the root from the denominator.
    https://calculat.io/en/number/cube-root/1-4/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    2/9∛6/3 ≈ 0.6057
    125/5125/8 = 0.625
    0.25≈ 0.63
    1/4∛2/2 ≈ 0.63
    8/272/3 ≈ 0.6667
    0.3≈ 0.6694
    1/3∛9/3 ≈ 0.6934
    Recalculate with different values ↑

    FAQ

    What is the cube root of 1/4?

    ∛(1/4) = ∛2/2 ≈ 0.63

    Why is ∛(1/4) = ∛2/2?

    ∛(1/4) = ∛1/∛4. Multiplying the numerator and the denominator by ∛(4²) = ∛16 makes the denominator a perfect cube: ∛16/∛64 = ∛16/4. Taking the cubes out of ∛16 and reducing gives ∛2/2. The value does not change; only the root leaves the denominator.

    Is ∛(1/4) a rational number?

    No: 1/4 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 ∛(1/4) is irrational; its decimal never ends and never repeats: ∛(1/4) ≈ 0.63.

    See Also