Cube Root of 297

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Cube root of

What is the cube root of 297?

Answer

∛297 =
3∛11 ≈ 6.6719

Real cube root: the only number whose cube is 297.

≈ — rounded to 4 decimal places. 297 is not the cube of a rational number, so ∛297 is irrational: its decimal expansion never ends and never repeats.

Prime factors
297 = (3 × 3 × 3) × 11 = 3³ × 11
Take out of the root
∛297 = ∛(3³ × 11) = 3∛11
Between cubes
6³ = 216 < 297 < 343 = 7³, so 6 < ∛297 < 7 and ∛297 ≈ 6.6719

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
290≈ 6.6191
292≈ 6.6343
2962∛37 ≈ 6.6644
2973∛11 ≈ 6.6719
300≈ 6.6943
323≈ 6.8612
3243∛12 ≈ 6.8683

FAQ

What is the cube root of 297?

∛297 = 3∛11 ≈ 6.6719

How to simplify ∛297?

Factor 297 into primes: 297 = 3 × 3 × 3 × 11. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛297 = ∛(3³ × 11) = 3∛11.

Is ∛297 a rational number?

No: 297 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 ∛297 is irrational; its decimal never ends and never repeats: ∛297 ≈ 6.6719.

See Also