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    Cube Root of 686

    Cube Root Calculator
    Cube root of

    What is the cube root of 686?

    Answer

    ∛686 =
    7∛2 ≈ 8.8194

    Real cube root: the only number whose cube is 686.

    ≈ — rounded to 4 decimal places. 686 is not the cube of a rational number, so ∛686 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    686 = 2 × (7 × 7 × 7) = 2 × 7³
    Take out of the root
    ∛686 = ∛(7³ × 2) = 7∛2
    Between cubes
    8³ = 512 < 686 < 729 = 9³, so 8 < ∛686 < 9 and ∛686 ≈ 8.8194

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    https://calculat.io/en/number/cube-root/686Copy
    <a href="https://calculat.io/en/number/cube-root/686">Cube Root of 686 (∛686): Exact Value and Decimal</a>Copy
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    Cube Root of 686 (∛686): Exact Value and Decimal. ∛686 = 7∛2 ≈ 8.8194. 686 = 7³ × 2, so 7 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/686/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    529≈ 8.0876
    620≈ 8.527
    6255∛5 ≈ 8.5499
    6867∛2 ≈ 8.8194
    700≈ 8.879
    7299
    730≈ 9.0041
    Recalculate with different values ↑

    FAQ

    What is the cube root of 686?

    ∛686 = 7∛2 ≈ 8.8194

    How to simplify ∛686?

    Factor 686 into primes: 686 = 2 × 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: ∛686 = ∛(7³ × 2) = 7∛2.

    Is ∛686 a rational number?

    No: 686 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 ∛686 is irrational; its decimal never ends and never repeats: ∛686 ≈ 8.8194.

    See Also