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    Cube Root of 10000

    Cube Root Calculator
    Cube root of

    What is the cube root of 10,000?

    Answer

    ∛10,000 =
    10∛10 ≈ 21.5443

    Real cube root: the only number whose cube is 10,000.

    ≈ — rounded to 4 decimal places. 10,000 is not the cube of a rational number, so ∛10,000 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    10,000 = (2 × 2 × 2) × 2 × (5 × 5 × 5) × 5 = 2⁴ × 5⁴
    Take out of the root
    ∛10,000 = ∛(2³ × 5³ × 10) = 2 × 5 × ∛10 = 10∛10
    Between cubes
    21³ = 9,261 < 10,000 < 10,648 = 22³, so 21 < ∛10,000 < 22 and ∛10,000 ≈ 21.5443

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    https://calculat.io/en/number/cube-root/10000Copy
    <a href="https://calculat.io/en/number/cube-root/10000">Cube Root of 10000 (∛10000): Exact Value and Decimal</a>Copy
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    Cube Root of 10000 (∛10000): Exact Value and Decimal. ∛10,000 = 10∛10 ≈ 21.5443. 10,000 = 10³ × 10, so 10 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/10000/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    9,26121
    9,621≈ 21.2687
    9,999≈ 21.5436
    10,00010∛10 ≈ 21.5443
    10,36812∛6 ≈ 21.8054
    10,64822
    11,025≈ 22.2566
    Recalculate with different values ↑

    FAQ

    What is the cube root of 10,000?

    ∛10,000 = 10∛10 ≈ 21.5443

    How to simplify ∛10,000?

    Factor 10,000 into primes: 10,000 = 2 × 2 × 2 × 2 × 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: ∛10,000 = ∛(2³ × 5³ × 10) = 10∛10.

    Is ∛10,000 a rational number?

    No: 10,000 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 ∛10,000 is irrational; its decimal never ends and never repeats: ∛10,000 ≈ 21.5443.

    See Also