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    Cube Root of 12800

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    Cube root of

    What is the cube root of 12,800?

    Answer

    ∛12,800 =
    8∛25 ≈ 23.3921

    Real cube root: the only number whose cube is 12,800.

    ≈ — rounded to 4 decimal places. 12,800 is not the cube of a rational number, so ∛12,800 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    12,800 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 5 × 5 = 2⁹ × 5²
    Take out of the root
    ∛12,800 = ∛((2³)³ × 25) = 2³ × ∛25 = 8∛25
    Between cubes
    23³ = 12,167 < 12,800 < 13,824 = 24³, so 23 < ∛12,800 < 24 and ∛12,800 ≈ 23.3921

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    https://calculat.io/en/number/cube-root/12800Copy
    <a href="https://calculat.io/en/number/cube-root/12800">Cube Root of 12800 (∛12800): Exact Value and Decimal</a>Copy
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    Cube Root of 12800 (∛12800): Exact Value and Decimal. ∛12,800 = 8∛25 ≈ 23.3921. 12,800 = 8³ × 25, so 8 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/12800/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    10,64822
    11,025≈ 22.2566
    12,16723
    12,8008∛25 ≈ 23.3921
    13,82424
    15,62525
    17,57626
    Recalculate with different values ↑

    FAQ

    What is the cube root of 12,800?

    ∛12,800 = 8∛25 ≈ 23.3921

    How to simplify ∛12,800?

    Factor 12,800 into primes: 12,800 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛12,800 = ∛((2³)³ × 25) = 8∛25.

    Is ∛12,800 a rational number?

    No: 12,800 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 ∛12,800 is irrational; its decimal never ends and never repeats: ∛12,800 ≈ 23.3921.

    See Also