Cube Root of 248

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Cube root of

What is the cube root of 248?

Answer

∛248 =
2∛31 ≈ 6.2828

Real cube root: the only number whose cube is 248.

≈ — rounded to 4 decimal places. 248 is not the cube of a rational number, so ∛248 is irrational: its decimal expansion never ends and never repeats.

Prime factors
248 = (2 × 2 × 2) × 31 = 2³ × 31
Take out of the root
∛248 = ∛(2³ × 31) = 2∛31
Between cubes
6³ = 216 < 248 < 343 = 7³, so 6 < ∛248 < 7 and ∛248 ≈ 6.2828

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2433∛9 ≈ 6.2403
245≈ 6.2573
247≈ 6.2743
2482∛31 ≈ 6.2828
2505∛2 ≈ 6.2996
255≈ 6.3413
2564∛4 ≈ 6.3496

FAQ

What is the cube root of 248?

∛248 = 2∛31 ≈ 6.2828

How to simplify ∛248?

Factor 248 into primes: 248 = 2 × 2 × 2 × 31. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛248 = ∛(2³ × 31) = 2∛31.

Is ∛248 a rational number?

No: 248 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 ∛248 is irrational; its decimal never ends and never repeats: ∛248 ≈ 6.2828.

See Also