Cube Root of 330

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Cube root of

What is the cube root of 330?

Answer

∛330 ≈
6.9104

Real cube root: the only number whose cube is 330.

≈ — rounded to 4 decimal places. 330 is not the cube of a rational number, so ∛330 is irrational: its decimal expansion never ends and never repeats.

Prime factors
330 = 2 × 3 × 5 × 11
Take out of the root
No prime appears three times, so ∛330 is already in simplest form.
Between cubes
6³ = 216 < 330 < 343 = 7³, so 6 < ∛330 < 7 and ∛330 ≈ 6.9104

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
325≈ 6.8753
327≈ 6.8894
329≈ 6.9034
330≈ 6.9104
331≈ 6.9174
3362∛42 ≈ 6.9521
3437

FAQ

What is the cube root of 330?

∛330 ≈ 6.9104

Can ∛330 be simplified?

No: no prime appears three times in 330, so its only cube factor is 1 and ∛330 is already in simplest form. Since 6³ = 216 < 330 < 343 = 7³, ∛330 lies between 6 and 7: ∛330 ≈ 6.9104.

Is ∛330 a rational number?

No: 330 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 ∛330 is irrational; its decimal never ends and never repeats: ∛330 ≈ 6.9104.

See Also