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    Cube Root of 432

    Cube Root Calculator
    Cube root of

    What is the cube root of 432?

    Answer

    ∛432 =
    6∛2 ≈ 7.5595

    Real cube root: the only number whose cube is 432.

    ≈ — rounded to 4 decimal places. 432 is not the cube of a rational number, so ∛432 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    432 = (2 × 2 × 2) × 2 × (3 × 3 × 3) = 2⁴ × 3³
    Take out of the root
    ∛432 = ∛(2³ × 3³ × 2) = 2 × 3 × ∛2 = 6∛2
    Between cubes
    7³ = 343 < 432 < 512 = 8³, so 7 < ∛432 < 8 and ∛432 ≈ 7.5595

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    https://calculat.io/en/number/cube-root/432Copy
    <a href="https://calculat.io/en/number/cube-root/432">Cube Root of 432 (∛432): Exact Value and Decimal</a>Copy
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    Cube Root of 432 (∛432): Exact Value and Decimal. ∛432 = 6∛2 ≈ 7.5595. 432 = 6³ × 2, so 6 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/432/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    3437
    3755∛3 ≈ 7.2112
    425≈ 7.5185
    4326∛2 ≈ 7.5595
    445≈ 7.6346
    4484∛7 ≈ 7.6517
    450≈ 7.6631
    Recalculate with different values ↑

    FAQ

    What is the cube root of 432?

    ∛432 = 6∛2 ≈ 7.5595

    How to simplify ∛432?

    Factor 432 into primes: 432 = 2 × 2 × 2 × 2 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛432 = ∛(2³ × 3³ × 2) = 6∛2.

    Is ∛432 a rational number?

    No: 432 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 ∛432 is irrational; its decimal never ends and never repeats: ∛432 ≈ 7.5595.

    See Also