Cube Root of 180

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Cube root of

What is the cube root of 180?

Answer

∛180 ≈
5.6462

Real cube root: the only number whose cube is 180.

≈ — rounded to 4 decimal places. 180 is not the cube of a rational number, so ∛180 is irrational: its decimal expansion never ends and never repeats.

Prime factors
180 = 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5
Take out of the root
No prime appears three times, so ∛180 is already in simplest form.
Between cubes
5³ = 125 < 180 < 216 = 6³, so 5 < ∛180 < 6 and ∛180 ≈ 5.6462

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Recalculate with different values ↑

Cube roots of nearby values

N∛N
173≈ 5.5721
175≈ 5.5934
178≈ 5.6252
180≈ 5.6462
182≈ 5.6671
187≈ 5.7185
1893∛7 ≈ 5.7388

FAQ

What is the cube root of 180?

∛180 ≈ 5.6462

Can ∛180 be simplified?

No: no prime appears three times in 180, so its only cube factor is 1 and ∛180 is already in simplest form. Since 5³ = 125 < 180 < 216 = 6³, ∛180 lies between 5 and 6: ∛180 ≈ 5.6462.

Is ∛180 a rational number?

No: 180 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 ∛180 is irrational; its decimal never ends and never repeats: ∛180 ≈ 5.6462.

See Also