Cube Root of 324

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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

Related Calculations

See Also

Recalculate with different values ↑

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

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