Cube Root of 225

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Cube root of

What is the cube root of 225?

Answer

∛225 ≈
6.0822

Real cube root: the only number whose cube is 225.

≈ — rounded to 4 decimal places. 225 is not the cube of a rational number, so ∛225 is irrational: its decimal expansion never ends and never repeats.

Prime factors
225 = 3 × 3 × 5 × 5 = 3² × 5²
Take out of the root
No prime appears three times, so ∛225 is already in simplest form.
Between cubes
6³ = 216 < 225 < 343 = 7³, so 6 < ∛225 < 7 and ∛225 ≈ 6.0822

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
220≈ 6.0368
222≈ 6.055
223≈ 6.0641
225≈ 6.0822
228≈ 6.1091
230≈ 6.1269
231≈ 6.1358

FAQ

What is the cube root of 225?

∛225 ≈ 6.0822

Can ∛225 be simplified?

No: no prime appears three times in 225, so its only cube factor is 1 and ∛225 is already in simplest form. Since 6³ = 216 < 225 < 343 = 7³, ∛225 lies between 6 and 7: ∛225 ≈ 6.0822.

Is ∛225 a rational number?

No: 225 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 ∛225 is irrational; its decimal never ends and never repeats: ∛225 ≈ 6.0822.

See Also