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What is the cube root of 2,400?

Answer

∛2,400 =
2∛300 ≈ 13.3887

Real cube root: the only number whose cube is 2,400.

≈ — rounded to 4 decimal places. 2,400 is not the cube of a rational number, so ∛2,400 is irrational: its decimal expansion never ends and never repeats.

Prime factors
2,400 = (2 × 2 × 2) × 2 × 2 × 3 × 5 × 5 = 2⁵ × 3 × 5²
Take out of the root
∛2,400 = ∛(2³ × 300) = 2∛300
Between cubes
13³ = 2,197 < 2,400 < 2,744 = 14³, so 13 < ∛2,400 < 14 and ∛2,400 ≈ 13.3887

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Recalculate with different values ↑

Cube roots of nearby values

N∛N
2,19713
2,2002∛275 ≈ 13.0059
2,300≈ 13.2001
2,4002∛300 ≈ 13.3887
2,4017∛7 ≈ 13.3905
2,450≈ 13.481
2,5926∛12 ≈ 13.7366

FAQ

What is the cube root of 2,400?

∛2,400 = 2∛300 ≈ 13.3887

How to simplify ∛2,400?

Factor 2,400 into primes: 2,400 = 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛2,400 = ∛(2³ × 300) = 2∛300.

Is ∛2,400 a rational number?

No: 2,400 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 ∛2,400 is irrational; its decimal never ends and never repeats: ∛2,400 ≈ 13.3887.

See Also