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    Cube Root of 32

    Cube Root Calculator
    Cube root of

    What is the cube root of 32?

    Answer

    ∛32 =
    2∛4 ≈ 3.1748

    Real cube root: the only number whose cube is 32.

    ≈ — rounded to 4 decimal places. 32 is not the cube of a rational number, so ∛32 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    32 = (2 × 2 × 2) × 2 × 2 = 2⁵
    Take out of the root
    ∛32 = ∛(2³ × 4) = 2∛4
    Between cubes
    3³ = 27 < 32 < 64 = 4³, so 3 < ∛32 < 4 and ∛32 ≈ 3.1748

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    https://calculat.io/en/number/cube-root/32Copy
    <a href="https://calculat.io/en/number/cube-root/32">Cube Root of 32 (∛32): Exact Value and Decimal - Calculatio</a>Copy
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    Cube Root of 32 (∛32): Exact Value and Decimal. ∛32 = 2∛4 ≈ 3.1748. 32 = 2³ × 4, so 2 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/32/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    29.5≈ 3.0899
    30≈ 3.1072
    31≈ 3.1414
    322∛4 ≈ 3.1748
    32.7683.2
    33≈ 3.2075
    34≈ 3.2396
    Recalculate with different values ↑

    FAQ

    What is the cube root of 32?

    ∛32 = 2∛4 ≈ 3.1748

    How to simplify ∛32?

    Factor 32 into primes: 32 = 2 × 2 × 2 × 2 × 2. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛32 = ∛(2³ × 4) = 2∛4.

    Is ∛32 a rational number?

    No: 32 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 ∛32 is irrational; its decimal never ends and never repeats: ∛32 ≈ 3.1748.

    See Also