Cube Root of 228

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Cube root of

What is the cube root of 228?

Answer

∛228 ≈
6.1091

Real cube root: the only number whose cube is 228.

≈ — rounded to 4 decimal places. 228 is not the cube of a rational number, so ∛228 is irrational: its decimal expansion never ends and never repeats.

Prime factors
228 = 2 × 2 × 3 × 19 = 2² × 3 × 19
Take out of the root
No prime appears three times, so ∛228 is already in simplest form.
Between cubes
6³ = 216 < 228 < 343 = 7³, so 6 < ∛228 < 7 and ∛228 ≈ 6.1091

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
222≈ 6.055
223≈ 6.0641
225≈ 6.0822
228≈ 6.1091
230≈ 6.1269
231≈ 6.1358
233≈ 6.1534

FAQ

What is the cube root of 228?

∛228 ≈ 6.1091

Can ∛228 be simplified?

No: no prime appears three times in 228, so its only cube factor is 1 and ∛228 is already in simplest form. Since 6³ = 216 < 228 < 343 = 7³, ∛228 lies between 6 and 7: ∛228 ≈ 6.1091.

Is ∛228 a rational number?

No: 228 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 ∛228 is irrational; its decimal never ends and never repeats: ∛228 ≈ 6.1091.

See Also