Cube Root of 288

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Cube root of

What is the cube root of 288?

Answer

∛288 =
2∛36 ≈ 6.6039

Real cube root: the only number whose cube is 288.

≈ — rounded to 4 decimal places. 288 is not the cube of a rational number, so ∛288 is irrational: its decimal expansion never ends and never repeats.

Prime factors
288 = (2 × 2 × 2) × 2 × 2 × 3 × 3 = 2⁵ × 3²
Take out of the root
∛288 = ∛(2³ × 36) = 2∛36
Between cubes
6³ = 216 < 288 < 343 = 7³, so 6 < ∛288 < 7 and ∛288 ≈ 6.6039

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
279≈ 6.5343
2802∛35 ≈ 6.5421
285≈ 6.5808
2882∛36 ≈ 6.6039
289≈ 6.6115
290≈ 6.6191
292≈ 6.6343

FAQ

What is the cube root of 288?

∛288 = 2∛36 ≈ 6.6039

How to simplify ∛288?

Factor 288 into primes: 288 = 2 × 2 × 2 × 2 × 2 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛288 = ∛(2³ × 36) = 2∛36.

Is ∛288 a rational number?

No: 288 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 ∛288 is irrational; its decimal never ends and never repeats: ∛288 ≈ 6.6039.

See Also