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    Cube Root of 81

    Cube Root Calculator
    Cube root of

    What is the cube root of 81?

    Answer

    ∛81 =
    3∛3 ≈ 4.3267

    Real cube root: the only number whose cube is 81.

    ≈ — rounded to 4 decimal places. 81 is not the cube of a rational number, so ∛81 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    81 = (3 × 3 × 3) × 3 = 3⁴
    Take out of the root
    ∛81 = ∛(3³ × 3) = 3∛3
    Between cubes
    4³ = 64 < 81 < 125 = 5³, so 4 < ∛81 < 5 and ∛81 ≈ 4.3267

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    https://calculat.io/en/number/cube-root/81Copy
    <a href="https://calculat.io/en/number/cube-root/81">Cube Root of 81 (∛81): Exact Value and Decimal - Calculatio</a>Copy
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    Cube Root of 81 (∛81): Exact Value and Decimal. ∛81 = 3∛3 ≈ 4.3267. 81 = 3³ × 3, so 3 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/81/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    78≈ 4.2727
    79≈ 4.2908
    802∛10 ≈ 4.3089
    813∛3 ≈ 4.3267
    82≈ 4.3445
    83≈ 4.3621
    84≈ 4.3795
    Recalculate with different values ↑

    FAQ

    What is the cube root of 81?

    ∛81 = 3∛3 ≈ 4.3267

    How to simplify ∛81?

    Factor 81 into primes: 81 = 3 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛81 = ∛(3³ × 3) = 3∛3.

    Is ∛81 a rational number?

    No: 81 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 ∛81 is irrational; its decimal never ends and never repeats: ∛81 ≈ 4.3267.

    See Also