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    Cube Root of 71

    Cube Root Calculator
    Cube root of

    What is the cube root of 71?

    Answer

    ∛71 ≈
    4.1408

    Real cube root: the only number whose cube is 71.

    ≈ — rounded to 4 decimal places. 71 is not the cube of a rational number, so ∛71 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    71 is a prime number: no triple of equal factors.
    Between cubes
    4³ = 64 < 71 < 125 = 5³, so 4 < ∛71 < 5 and ∛71 ≈ 4.1408

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    https://calculat.io/en/number/cube-root/71Copy
    <a href="https://calculat.io/en/number/cube-root/71">Cube Root of 71 (∛71): Exact Value and Decimal - Calculatio</a>Copy
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    Cube Root of 71 (∛71): Exact Value and Decimal. ∛71 ≈ 4.1408. 71 has no cube factor but 1, so ∛71 is already simplest; it lies between 4 and 5.
    https://calculat.io/en/number/cube-root/71/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    68≈ 4.0817
    69≈ 4.1016
    70≈ 4.1213
    71≈ 4.1408
    722∛9 ≈ 4.1602
    73≈ 4.1793
    74≈ 4.1983
    Recalculate with different values ↑

    FAQ

    What is the cube root of 71?

    ∛71 ≈ 4.1408

    Can ∛71 be simplified?

    No: no prime appears three times in 71, so its only cube factor is 1 and ∛71 is already in simplest form. Since 4³ = 64 < 71 < 125 = 5³, ∛71 lies between 4 and 5: ∛71 ≈ 4.1408.

    Is ∛71 a rational number?

    No: 71 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 ∛71 is irrational; its decimal never ends and never repeats: ∛71 ≈ 4.1408.

    See Also