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    Cube Root of 2000

    Cube Root Calculator
    Cube root of

    What is the cube root of 2,000?

    Answer

    ∛2,000 =
    10∛2 ≈ 12.5992

    Real cube root: the only number whose cube is 2,000.

    ≈ — rounded to 4 decimal places. 2,000 is not the cube of a rational number, so ∛2,000 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    2,000 = (2 × 2 × 2) × 2 × (5 × 5 × 5) = 2⁴ × 5³
    Take out of the root
    ∛2,000 = ∛(2³ × 5³ × 2) = 2 × 5 × ∛2 = 10∛2
    Between cubes
    12³ = 1,728 < 2,000 < 2,197 = 13³, so 12 < ∛2,000 < 13 and ∛2,000 ≈ 12.5992

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    https://calculat.io/en/number/cube-root/2000Copy
    <a href="https://calculat.io/en/number/cube-root/2000">Cube Root of 2000 (∛2000): Exact Value and Decimal</a>Copy
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    Cube Root of 2000 (∛2000): Exact Value and Decimal. ∛2,000 = 10∛2 ≈ 12.5992. 2,000 = 10³ × 2, so 10 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/2000/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    1,729≈ 12.0023
    1,738≈ 12.0231
    1,8002∛225 ≈ 12.1644
    2,00010∛2 ≈ 12.5992
    2,007≈ 12.6139
    2,0242∛253 ≈ 12.6494
    2,19713
    Recalculate with different values ↑

    FAQ

    What is the cube root of 2,000?

    ∛2,000 = 10∛2 ≈ 12.5992

    How to simplify ∛2,000?

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

    Is ∛2,000 a rational number?

    No: 2,000 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 ∛2,000 is irrational; its decimal never ends and never repeats: ∛2,000 ≈ 12.5992.

    See Also