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    Cube Root of 1024

    Cube Root Calculator
    Cube root of

    What is the cube root of 1,024?

    Answer

    ∛1,024 =
    8∛2 ≈ 10.0794

    Real cube root: the only number whose cube is 1,024.

    ≈ — rounded to 4 decimal places. 1,024 is not the cube of a rational number, so ∛1,024 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    1,024 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 2 = 2¹⁰
    Take out of the root
    ∛1,024 = ∛((2³)³ × 2) = 2³ × ∛2 = 8∛2
    Between cubes
    10³ = 1,000 < 1,024 < 1,331 = 11³, so 10 < ∛1,024 < 11 and ∛1,024 ≈ 10.0794

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    https://calculat.io/en/number/cube-root/1024Copy
    <a href="https://calculat.io/en/number/cube-root/1024">Cube Root of 1024 (∛1024): Exact Value and Decimal</a>Copy
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    Cube Root of 1024 (∛1024): Exact Value and Decimal. ∛1,024 = 8∛2 ≈ 10.0794. 1,024 = 8³ × 2, so 8 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/1024/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    9993∛37 ≈ 9.9967
    1,00010
    1,001≈ 10.0033
    1,0248∛2 ≈ 10.0794
    1,0297∛3 ≈ 10.0957
    1,0806∛5 ≈ 10.2599
    1,089≈ 10.2883
    Recalculate with different values ↑

    FAQ

    What is the cube root of 1,024?

    ∛1,024 = 8∛2 ≈ 10.0794

    How to simplify ∛1,024?

    Factor 1,024 into primes: 1,024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,024 = ∛((2³)³ × 2) = 8∛2.

    Is ∛1,024 a rational number?

    No: 1,024 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 ∛1,024 is irrational; its decimal never ends and never repeats: ∛1,024 ≈ 10.0794.

    See Also