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What is the cube root of 2,401?

Answer

∛2,401 =
7∛7 ≈ 13.3905

Real cube root: the only number whose cube is 2,401.

≈ — rounded to 4 decimal places. 2,401 is not the cube of a rational number, so ∛2,401 is irrational: its decimal expansion never ends and never repeats.

Prime factors
2,401 = (7 × 7 × 7) × 7 = 7⁴
Take out of the root
∛2,401 = ∛(7³ × 7) = 7∛7
Between cubes
13³ = 2,197 < 2,401 < 2,744 = 14³, so 13 < ∛2,401 < 14 and ∛2,401 ≈ 13.3905

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Recalculate with different values ↑

Cube roots of nearby values

N∛N
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
2,74414

FAQ

What is the cube root of 2,401?

∛2,401 = 7∛7 ≈ 13.3905

How to simplify ∛2,401?

Factor 2,401 into primes: 2,401 = 7 × 7 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛2,401 = ∛(7³ × 7) = 7∛7.

Is ∛2,401 a rational number?

No: 2,401 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 ∛2,401 is irrational; its decimal never ends and never repeats: ∛2,401 ≈ 13.3905.

See Also