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    Cube Root of 324

    Cube Root Calculator
    Cube root of

    What is the cube root of 324?

    Answer

    ∛324 =
    3∛12 ≈ 6.8683

    Real cube root: the only number whose cube is 324.

    ≈ — rounded to 4 decimal places. 324 is not the cube of a rational number, so ∛324 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    324 = 2 × 2 × (3 × 3 × 3) × 3 = 2² × 3⁴
    Take out of the root
    ∛324 = ∛(3³ × 12) = 3∛12
    Between cubes
    6³ = 216 < 324 < 343 = 7³, so 6 < ∛324 < 7 and ∛324 ≈ 6.8683

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    https://calculat.io/en/number/cube-root/324Copy
    <a href="https://calculat.io/en/number/cube-root/324">Cube Root of 324 (∛324): Exact Value and Decimal</a>Copy
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    Cube Root of 324 (∛324): Exact Value and Decimal. ∛324 = 3∛12 ≈ 6.8683. 324 = 3³ × 12, so 3 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/324/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    2973∛11 ≈ 6.6719
    300≈ 6.6943
    323≈ 6.8612
    3243∛12 ≈ 6.8683
    325≈ 6.8753
    327≈ 6.8894
    329≈ 6.9034
    Recalculate with different values ↑

    FAQ

    What is the cube root of 324?

    ∛324 = 3∛12 ≈ 6.8683

    How to simplify ∛324?

    Factor 324 into primes: 324 = 2 × 2 × 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: ∛324 = ∛(3³ × 12) = 3∛12.

    Is ∛324 a rational number?

    No: 324 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 ∛324 is irrational; its decimal never ends and never repeats: ∛324 ≈ 6.8683.

    See Also