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    Cube Root of 2400

    Cube Root Calculator
    Cube root of

    What is the cube root of 2,400?

    Answer

    ∛2,400 =
    2∛300 ≈ 13.3887

    Real cube root: the only number whose cube is 2,400.

    ≈ — rounded to 4 decimal places. 2,400 is not the cube of a rational number, so ∛2,400 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    2,400 = (2 × 2 × 2) × 2 × 2 × 3 × 5 × 5 = 2⁵ × 3 × 5²
    Take out of the root
    ∛2,400 = ∛(2³ × 300) = 2∛300
    Between cubes
    13³ = 2,197 < 2,400 < 2,744 = 14³, so 13 < ∛2,400 < 14 and ∛2,400 ≈ 13.3887

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    https://calculat.io/en/number/cube-root/2400Copy
    <a href="https://calculat.io/en/number/cube-root/2400">Cube Root of 2400 (∛2400): Exact Value and Decimal</a>Copy
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    Cube Root of 2400 (∛2400): Exact Value and Decimal. ∛2,400 = 2∛300 ≈ 13.3887. 2,400 = 2³ × 300, so 2 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/2400/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    2,19713
    2,2002∛275 ≈ 13.0059
    2,300≈ 13.2001
    2,4002∛300 ≈ 13.3887
    2,4017∛7 ≈ 13.3905
    2,450≈ 13.481
    2,5926∛12 ≈ 13.7366
    Recalculate with different values ↑

    FAQ

    What is the cube root of 2,400?

    ∛2,400 = 2∛300 ≈ 13.3887

    How to simplify ∛2,400?

    Factor 2,400 into primes: 2,400 = 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛2,400 = ∛(2³ × 300) = 2∛300.

    Is ∛2,400 a rational number?

    No: 2,400 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 ∛2,400 is irrational; its decimal never ends and never repeats: ∛2,400 ≈ 13.3887.

    See Also