Cube Root of 2880

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What is the cube root of 2,880?

Answer

∛2,880 =
4∛45 ≈ 14.2276

Real cube root: the only number whose cube is 2,880.

≈ — rounded to 4 decimal places. 2,880 is not the cube of a rational number, so ∛2,880 is irrational: its decimal expansion never ends and never repeats.

Prime factors
2,880 = (2 × 2 × 2) × (2 × 2 × 2) × 3 × 3 × 5 = 2⁶ × 3² × 5
Take out of the root
∛2,880 = ∛((2³)² × 45) = 2² × ∛45 = 4∛45
Between cubes
14³ = 2,744 < 2,880 < 3,375 = 15³, so 14 < ∛2,880 < 15 and ∛2,880 ≈ 14.2276

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2,450≈ 13.481
2,5926∛12 ≈ 13.7366
2,74414
2,8804∛45 ≈ 14.2276
2,917≈ 14.2882
3,0877∛9 ≈ 14.5606
3,1255∛25 ≈ 14.6201

FAQ

What is the cube root of 2,880?

∛2,880 = 4∛45 ≈ 14.2276

How to simplify ∛2,880?

Factor 2,880 into primes: 2,880 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛2,880 = ∛((2³)² × 45) = 4∛45.

Is ∛2,880 a rational number?

No: 2,880 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 ∛2,880 is irrational; its decimal never ends and never repeats: ∛2,880 ≈ 14.2276.

See Also