Cube Root of 231

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Cube root of

What is the cube root of 231?

Answer

∛231 ≈
6.1358

Real cube root: the only number whose cube is 231.

≈ — rounded to 4 decimal places. 231 is not the cube of a rational number, so ∛231 is irrational: its decimal expansion never ends and never repeats.

Prime factors
231 = 3 × 7 × 11
Take out of the root
No prime appears three times, so ∛231 is already in simplest form.
Between cubes
6³ = 216 < 231 < 343 = 7³, so 6 < ∛231 < 7 and ∛231 ≈ 6.1358

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
225≈ 6.0822
228≈ 6.1091
230≈ 6.1269
231≈ 6.1358
233≈ 6.1534
238≈ 6.1972
239≈ 6.2058

FAQ

What is the cube root of 231?

∛231 ≈ 6.1358

Can ∛231 be simplified?

No: no prime appears three times in 231, so its only cube factor is 1 and ∛231 is already in simplest form. Since 6³ = 216 < 231 < 343 = 7³, ∛231 lies between 6 and 7: ∛231 ≈ 6.1358.

Is ∛231 a rational number?

No: 231 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 ∛231 is irrational; its decimal never ends and never repeats: ∛231 ≈ 6.1358.

See Also