Cube Root of 296

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Cube root of

What is the cube root of 296?

Answer

∛296 =
2∛37 ≈ 6.6644

Real cube root: the only number whose cube is 296.

≈ — rounded to 4 decimal places. 296 is not the cube of a rational number, so ∛296 is irrational: its decimal expansion never ends and never repeats.

Prime factors
296 = (2 × 2 × 2) × 37 = 2³ × 37
Take out of the root
∛296 = ∛(2³ × 37) = 2∛37
Between cubes
6³ = 216 < 296 < 343 = 7³, so 6 < ∛296 < 7 and ∛296 ≈ 6.6644

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
289≈ 6.6115
290≈ 6.6191
292≈ 6.6343
2962∛37 ≈ 6.6644
2973∛11 ≈ 6.6719
300≈ 6.6943
323≈ 6.8612

FAQ

What is the cube root of 296?

∛296 = 2∛37 ≈ 6.6644

How to simplify ∛296?

Factor 296 into primes: 296 = 2 × 2 × 2 × 37. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛296 = ∛(2³ × 37) = 2∛37.

Is ∛296 a rational number?

No: 296 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 ∛296 is irrational; its decimal never ends and never repeats: ∛296 ≈ 6.6644.

See Also