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    Cube Root of 40

    Cube Root Calculator
    Cube root of

    What is the cube root of 40?

    Answer

    ∛40 =
    2∛5 ≈ 3.42

    Real cube root: the only number whose cube is 40.

    ≈ — rounded to 4 decimal places. 40 is not the cube of a rational number, so ∛40 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    40 = (2 × 2 × 2) × 5 = 2³ × 5
    Take out of the root
    ∛40 = ∛(2³ × 5) = 2∛5
    Between cubes
    3³ = 27 < 40 < 64 = 4³, so 3 < ∛40 < 4 and ∛40 ≈ 3.42

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    https://calculat.io/en/number/cube-root/40Copy
    <a href="https://calculat.io/en/number/cube-root/40">Cube Root of 40 (∛40): Exact Value and Decimal - Calculatio</a>Copy
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    Cube Root of 40 (∛40): Exact Value and Decimal. ∛40 = 2∛5 ≈ 3.42. 40 = 2³ × 5, so 2 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/40/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    37≈ 3.3322
    38≈ 3.362
    39≈ 3.3912
    402∛5 ≈ 3.42
    41≈ 3.4482
    42≈ 3.476
    42.8753.5
    Recalculate with different values ↑

    FAQ

    What is the cube root of 40?

    ∛40 = 2∛5 ≈ 3.42

    How to simplify ∛40?

    Factor 40 into primes: 40 = 2 × 2 × 2 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛40 = ∛(2³ × 5) = 2∛5.

    Is ∛40 a rational number?

    No: 40 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 ∛40 is irrational; its decimal never ends and never repeats: ∛40 ≈ 3.42.

    See Also