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    Cube Root of 1029

    Cube Root Calculator
    Cube root of

    What is the cube root of 1,029?

    Answer

    ∛1,029 =
    7∛3 ≈ 10.0957

    Real cube root: the only number whose cube is 1,029.

    ≈ — rounded to 4 decimal places. 1,029 is not the cube of a rational number, so ∛1,029 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    1,029 = 3 × (7 × 7 × 7) = 3 × 7³
    Take out of the root
    ∛1,029 = ∛(7³ × 3) = 7∛3
    Between cubes
    10³ = 1,000 < 1,029 < 1,331 = 11³, so 10 < ∛1,029 < 11 and ∛1,029 ≈ 10.0957

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    https://calculat.io/en/number/cube-root/1029Copy
    <a href="https://calculat.io/en/number/cube-root/1029">Cube Root of 1029 (∛1029): Exact Value and Decimal</a>Copy
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    Cube Root of 1029 (∛1029): Exact Value and Decimal. ∛1,029 = 7∛3 ≈ 10.0957. 1,029 = 7³ × 3, so 7 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/1029/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    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
    1,1255∛9 ≈ 10.4004
    Recalculate with different values ↑

    FAQ

    What is the cube root of 1,029?

    ∛1,029 = 7∛3 ≈ 10.0957

    How to simplify ∛1,029?

    Factor 1,029 into primes: 1,029 = 3 × 7 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,029 = ∛(7³ × 3) = 7∛3.

    Is ∛1,029 a rational number?

    No: 1,029 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 ∛1,029 is irrational; its decimal never ends and never repeats: ∛1,029 ≈ 10.0957.

    See Also