Cube Root of 250

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Cube root of

What is the cube root of 250?

Answer

∛250 =
5∛2 ≈ 6.2996

Real cube root: the only number whose cube is 250.

≈ — rounded to 4 decimal places. 250 is not the cube of a rational number, so ∛250 is irrational: its decimal expansion never ends and never repeats.

Prime factors
250 = 2 × (5 × 5 × 5) = 2 × 5³
Take out of the root
∛250 = ∛(5³ × 2) = 5∛2
Between cubes
6³ = 216 < 250 < 343 = 7³, so 6 < ∛250 < 7 and ∛250 ≈ 6.2996

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
245≈ 6.2573
247≈ 6.2743
2482∛31 ≈ 6.2828
2505∛2 ≈ 6.2996
255≈ 6.3413
2564∛4 ≈ 6.3496
257≈ 6.3579

FAQ

What is the cube root of 250?

∛250 = 5∛2 ≈ 6.2996

How to simplify ∛250?

Factor 250 into primes: 250 = 2 × 5 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛250 = ∛(5³ × 2) = 5∛2.

Is ∛250 a rational number?

No: 250 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 ∛250 is irrational; its decimal never ends and never repeats: ∛250 ≈ 6.2996.

See Also