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    Cube Root of 240

    Cube Root Calculator
    Cube root of

    What is the cube root of 240?

    Answer

    ∛240 =
    2∛30 ≈ 6.2145

    Real cube root: the only number whose cube is 240.

    ≈ — rounded to 4 decimal places. 240 is not the cube of a rational number, so ∛240 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    240 = (2 × 2 × 2) × 2 × 3 × 5 = 2⁴ × 3 × 5
    Take out of the root
    ∛240 = ∛(2³ × 30) = 2∛30
    Between cubes
    6³ = 216 < 240 < 343 = 7³, so 6 < ∛240 < 7 and ∛240 ≈ 6.2145

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    https://calculat.io/en/number/cube-root/240Copy
    <a href="https://calculat.io/en/number/cube-root/240">Cube Root of 240 (∛240): Exact Value and Decimal</a>Copy
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    Cube Root of 240 (∛240): Exact Value and Decimal. ∛240 = 2∛30 ≈ 6.2145. 240 = 2³ × 30, so 2 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/240/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    233≈ 6.1534
    238≈ 6.1972
    239≈ 6.2058
    2402∛30 ≈ 6.2145
    242≈ 6.2317
    2433∛9 ≈ 6.2403
    245≈ 6.2573
    Recalculate with different values ↑

    FAQ

    What is the cube root of 240?

    ∛240 = 2∛30 ≈ 6.2145

    How to simplify ∛240?

    Factor 240 into primes: 240 = 2 × 2 × 2 × 2 × 3 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛240 = ∛(2³ × 30) = 2∛30.

    Is ∛240 a rational number?

    No: 240 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 ∛240 is irrational; its decimal never ends and never repeats: ∛240 ≈ 6.2145.

    See Also