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    Cube Root of 5/4

    Cube Root Calculator
    Cube root of

    What is the cube root of 5/4?

    Answer

    ∛(5/4) =
    ∛10/2 ≈ 1.0772

    Real cube root: the only number whose cube is 5/4.

    ≈ — rounded to 4 decimal places. 5/4 is not the cube of a rational number, so ∛(5/4) is irrational: its decimal expansion never ends and never repeats.

    5/4 = 1.25.

    Root of a fraction
    ∛(5/4) = ∛5/∛4
    Multiply by ∛(4²) = ∛16
    ∛5/∛4 = ∛80/∛64 = ∛80/4
    Take out of the root
    ∛80/4 = ∛(2³ × 10)/4 = 2∛10/4 = ∛10/2 ≈ 1.0772

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    https://calculat.io/en/number/cube-root/5-4Copy
    <a href="https://calculat.io/en/number/cube-root/5-4">Cube Root of 5/4 (∛(5/4)): Exact Value and Decimal</a>Copy
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    Cube Root of 5/4 (∛(5/4)): Exact Value and Decimal. ∛(5/4) = ∛10/2 ≈ 1.0772. ∛(5/4) = ∛5/∛4; multiplying by ∛16 clears the root from the denominator.
    https://calculat.io/en/number/cube-root/5-4/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    1.2≈ 1.0627
    1.21≈ 1.0656
    1.25≈ 1.0772
    5/4∛10/2 ≈ 1.0772
    1.33≈ 1.0997
    1.3311.1
    4/3∛36/3 ≈ 1.1006
    Recalculate with different values ↑

    FAQ

    What is the cube root of 5/4?

    ∛(5/4) = ∛10/2 ≈ 1.0772

    Why is ∛(5/4) = ∛10/2?

    ∛(5/4) = ∛5/∛4. Multiplying the numerator and the denominator by ∛(4²) = ∛16 makes the denominator a perfect cube: ∛80/∛64 = ∛80/4. Taking the cubes out of ∛80 and reducing gives ∛10/2. The value does not change; only the root leaves the denominator.

    Is ∛(5/4) a rational number?

    No: 5/4 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 ∛(5/4) is irrational; its decimal never ends and never repeats: ∛(5/4) ≈ 1.0772.

    See Also