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    Cube Root of 625

    Cube Root Calculator
    Cube root of

    What is the cube root of 625?

    Answer

    ∛625 =
    5∛5 ≈ 8.5499

    Real cube root: the only number whose cube is 625.

    ≈ — rounded to 4 decimal places. 625 is not the cube of a rational number, so ∛625 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    625 = (5 × 5 × 5) × 5 = 5⁴
    Take out of the root
    ∛625 = ∛(5³ × 5) = 5∛5
    Between cubes
    8³ = 512 < 625 < 729 = 9³, so 8 < ∛625 < 9 and ∛625 ≈ 8.5499

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    https://calculat.io/en/number/cube-root/625Copy
    <a href="https://calculat.io/en/number/cube-root/625">Cube Root of 625 (∛625): Exact Value and Decimal</a>Copy
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    Cube Root of 625 (∛625): Exact Value and Decimal. ∛625 = 5∛5 ≈ 8.5499. 625 = 5³ × 5, so 5 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/625/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    527≈ 8.0774
    529≈ 8.0876
    620≈ 8.527
    6255∛5 ≈ 8.5499
    6867∛2 ≈ 8.8194
    700≈ 8.879
    7299
    Recalculate with different values ↑

    FAQ

    What is the cube root of 625?

    ∛625 = 5∛5 ≈ 8.5499

    How to simplify ∛625?

    Factor 625 into primes: 625 = 5 × 5 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛625 = ∛(5³ × 5) = 5∛5.

    Is ∛625 a rational number?

    No: 625 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 ∛625 is irrational; its decimal never ends and never repeats: ∛625 ≈ 8.5499.

    See Also