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    Cube Root of 3/4

    Cube Root Calculator
    Cube root of

    What is the cube root of 3/4?

    Answer

    ∛(3/4) =
    ∛6/2 ≈ 0.9086

    Real cube root: the only number whose cube is 3/4.

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

    Root of a fraction
    ∛(3/4) = ∛3/∛4
    Multiply by ∛(4²) = ∛16
    ∛3/∛4 = ∛48/∛64 = ∛48/4
    Take out of the root
    ∛48/4 = ∛(2³ × 6)/4 = 2∛6/4 = ∛6/2 ≈ 0.9086

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    https://calculat.io/en/number/cube-root/3-4Copy
    <a href="https://calculat.io/en/number/cube-root/3-4">Cube Root of 3/4 (∛(3/4)): Exact Value and Decimal</a>Copy
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    Cube Root of 3/4 (∛(3/4)): Exact Value and Decimal. ∛(3/4) = ∛6/2 ≈ 0.9086. ∛(3/4) = ∛3/∛4; multiplying by ∛16 clears the root from the denominator.
    https://calculat.io/en/number/cube-root/3-4/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    512/7298/9 ≈ 0.8889
    0.7290.9
    729/10009/10 = 0.9
    3/4∛6/2 ≈ 0.9086
    0.8≈ 0.9283
    4/5∛100/5 ≈ 0.9283
    11
    Recalculate with different values ↑

    FAQ

    What is the cube root of 3/4?

    ∛(3/4) = ∛6/2 ≈ 0.9086

    Why is ∛(3/4) = ∛6/2?

    ∛(3/4) = ∛3/∛4. Multiplying the numerator and the denominator by ∛(4²) = ∛16 makes the denominator a perfect cube: ∛48/∛64 = ∛48/4. Taking the cubes out of ∛48 and reducing gives ∛6/2. The value does not change; only the root leaves the denominator.

    Is ∛(3/4) a rational number?

    No: 3/4 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 ∛(3/4) is irrational; its decimal never ends and never repeats: ∛(3/4) ≈ 0.9086.

    See Also