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    Cube Root of 72

    Cube Root Calculator
    Cube root of

    What is the cube root of 72?

    Answer

    ∛72 =
    2∛9 ≈ 4.1602

    Real cube root: the only number whose cube is 72.

    ≈ — rounded to 4 decimal places. 72 is not the cube of a rational number, so ∛72 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    72 = (2 × 2 × 2) × 3 × 3 = 2³ × 3²
    Take out of the root
    ∛72 = ∛(2³ × 9) = 2∛9
    Between cubes
    4³ = 64 < 72 < 125 = 5³, so 4 < ∛72 < 5 and ∛72 ≈ 4.1602

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    https://calculat.io/en/number/cube-root/72Copy
    <a href="https://calculat.io/en/number/cube-root/72">Cube Root of 72 (∛72): Exact Value and Decimal - Calculatio</a>Copy
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    Cube Root of 72 (∛72): Exact Value and Decimal. ∛72 = 2∛9 ≈ 4.1602. 72 = 2³ × 9, so 2 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/72/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    69≈ 4.1016
    70≈ 4.1213
    71≈ 4.1408
    722∛9 ≈ 4.1602
    73≈ 4.1793
    74≈ 4.1983
    75≈ 4.2172
    Recalculate with different values ↑

    FAQ

    What is the cube root of 72?

    ∛72 = 2∛9 ≈ 4.1602

    How to simplify ∛72?

    Factor 72 into primes: 72 = 2 × 2 × 2 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛72 = ∛(2³ × 9) = 2∛9.

    Is ∛72 a rational number?

    No: 72 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 ∛72 is irrational; its decimal never ends and never repeats: ∛72 ≈ 4.1602.

    See Also