Cube Root of 208

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Cube root of

What is the cube root of 208?

Answer

∛208 =
2∛26 ≈ 5.925

Real cube root: the only number whose cube is 208.

≈ — rounded to 4 decimal places. 208 is not the cube of a rational number, so ∛208 is irrational: its decimal expansion never ends and never repeats.

Prime factors
208 = (2 × 2 × 2) × 2 × 13 = 2⁴ × 13
Take out of the root
∛208 = ∛(2³ × 26) = 2∛26
Between cubes
5³ = 125 < 208 < 216 = 6³, so 5 < ∛208 < 6 and ∛208 ≈ 5.925

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Cube roots of nearby values

N∛N
2002∛25 ≈ 5.848
201≈ 5.8578
207≈ 5.9155
2082∛26 ≈ 5.925
213≈ 5.9721
2166
217≈ 6.0092

FAQ

What is the cube root of 208?

∛208 = 2∛26 ≈ 5.925

How to simplify ∛208?

Factor 208 into primes: 208 = 2 × 2 × 2 × 2 × 13. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛208 = ∛(2³ × 26) = 2∛26.

Is ∛208 a rational number?

No: 208 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 ∛208 is irrational; its decimal never ends and never repeats: ∛208 ≈ 5.925.

See Also