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    Cube Root of 4500

    Cube Root Calculator
    Cube root of

    What is the cube root of 4,500?

    Answer

    ∛4,500 =
    5∛36 ≈ 16.5096

    Real cube root: the only number whose cube is 4,500.

    ≈ — rounded to 4 decimal places. 4,500 is not the cube of a rational number, so ∛4,500 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    4,500 = 2 × 2 × 3 × 3 × (5 × 5 × 5) = 2² × 3² × 5³
    Take out of the root
    ∛4,500 = ∛(5³ × 36) = 5∛36
    Between cubes
    16³ = 4,096 < 4,500 < 4,913 = 17³, so 16 < ∛4,500 < 17 and ∛4,500 ≈ 16.5096

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    https://calculat.io/en/number/cube-root/4500Copy
    <a href="https://calculat.io/en/number/cube-root/4500">Cube Root of 4500 (∛4500): Exact Value and Decimal</a>Copy
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    Cube Root of 4500 (∛4500): Exact Value and Decimal. ∛4,500 = 5∛36 ≈ 16.5096. 4,500 = 5³ × 36, so 5 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/4500/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    4,045≈ 15.9333
    4,09616
    4,225≈ 16.1662
    4,5005∛36 ≈ 16.5096
    4,900≈ 16.985
    4,91317
    5,382≈ 17.5246
    Recalculate with different values ↑

    FAQ

    What is the cube root of 4,500?

    ∛4,500 = 5∛36 ≈ 16.5096

    How to simplify ∛4,500?

    Factor 4,500 into primes: 4,500 = 2 × 2 × 3 × 3 × 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: ∛4,500 = ∛(5³ × 36) = 5∛36.

    Is ∛4,500 a rational number?

    No: 4,500 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 ∛4,500 is irrational; its decimal never ends and never repeats: ∛4,500 ≈ 16.5096.

    See Also