Cube Root of 2592

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What is the cube root of 2,592?

Answer

∛2,592 =
6∛12 ≈ 13.7366

Real cube root: the only number whose cube is 2,592.

≈ — rounded to 4 decimal places. 2,592 is not the cube of a rational number, so ∛2,592 is irrational: its decimal expansion never ends and never repeats.

Prime factors
2,592 = (2 × 2 × 2) × 2 × 2 × (3 × 3 × 3) × 3 = 2⁵ × 3⁴
Take out of the root
∛2,592 = ∛(2³ × 3³ × 12) = 2 × 3 × ∛12 = 6∛12
Between cubes
13³ = 2,197 < 2,592 < 2,744 = 14³, so 13 < ∛2,592 < 14 and ∛2,592 ≈ 13.7366

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2,4002∛300 ≈ 13.3887
2,4017∛7 ≈ 13.3905
2,450≈ 13.481
2,5926∛12 ≈ 13.7366
2,74414
2,8804∛45 ≈ 14.2276
2,917≈ 14.2882

FAQ

What is the cube root of 2,592?

∛2,592 = 6∛12 ≈ 13.7366

How to simplify ∛2,592?

Factor 2,592 into primes: 2,592 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛2,592 = ∛(2³ × 3³ × 12) = 6∛12.

Is ∛2,592 a rational number?

No: 2,592 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 ∛2,592 is irrational; its decimal never ends and never repeats: ∛2,592 ≈ 13.7366.

See Also