Cube Root of 256

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Cube root of

What is the cube root of 256?

Answer

∛256 =
4∛4 ≈ 6.3496

Real cube root: the only number whose cube is 256.

≈ — rounded to 4 decimal places. 256 is not the cube of a rational number, so ∛256 is irrational: its decimal expansion never ends and never repeats.

Prime factors
256 = (2 × 2 × 2) × (2 × 2 × 2) × 2 × 2 = 2⁸
Take out of the root
∛256 = ∛((2³)² × 4) = 2² × ∛4 = 4∛4
Between cubes
6³ = 216 < 256 < 343 = 7³, so 6 < ∛256 < 7 and ∛256 ≈ 6.3496

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2482∛31 ≈ 6.2828
2505∛2 ≈ 6.2996
255≈ 6.3413
2564∛4 ≈ 6.3496
257≈ 6.3579
258≈ 6.3661
276≈ 6.5108

FAQ

What is the cube root of 256?

∛256 = 4∛4 ≈ 6.3496

How to simplify ∛256?

Factor 256 into primes: 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛256 = ∛((2³)² × 4) = 4∛4.

Is ∛256 a rational number?

No: 256 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 ∛256 is irrational; its decimal never ends and never repeats: ∛256 ≈ 6.3496.

See Also