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    Cube Root of 102

    Cube Root Calculator
    Cube root of

    What is the cube root of 102?

    Answer

    ∛102 ≈
    4.6723

    Real cube root: the only number whose cube is 102.

    ≈ — rounded to 4 decimal places. 102 is not the cube of a rational number, so ∛102 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    102 = 2 × 3 × 17
    Take out of the root
    No prime appears three times, so ∛102 is already in simplest form.
    Between cubes
    4³ = 64 < 102 < 125 = 5³, so 4 < ∛102 < 5 and ∛102 ≈ 4.6723

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    https://calculat.io/en/number/cube-root/102Copy
    <a href="https://calculat.io/en/number/cube-root/102">Cube Root of 102 (∛102): Exact Value and Decimal</a>Copy
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    Cube Root of 102 (∛102): Exact Value and Decimal. ∛102 ≈ 4.6723. 102 has no cube factor but 1, so ∛102 is already simplest; it lies between 4 and 5.
    https://calculat.io/en/number/cube-root/102/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    98≈ 4.6104
    99≈ 4.6261
    100≈ 4.6416
    102≈ 4.6723
    103≈ 4.6875
    107≈ 4.7475
    1083∛4 ≈ 4.7622
    Recalculate with different values ↑

    FAQ

    What is the cube root of 102?

    ∛102 ≈ 4.6723

    Can ∛102 be simplified?

    No: no prime appears three times in 102, so its only cube factor is 1 and ∛102 is already in simplest form. Since 4³ = 64 < 102 < 125 = 5³, ∛102 lies between 4 and 5: ∛102 ≈ 4.6723.

    Is ∛102 a rational number?

    No: 102 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 ∛102 is irrational; its decimal never ends and never repeats: ∛102 ≈ 4.6723.

    See Also