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What is the cube root of 2,024?

Answer

∛2,024 =
2∛253 ≈ 12.6494

Real cube root: the only number whose cube is 2,024.

≈ — rounded to 4 decimal places. 2,024 is not the cube of a rational number, so ∛2,024 is irrational: its decimal expansion never ends and never repeats.

Prime factors
2,024 = (2 × 2 × 2) × 11 × 23 = 2³ × 11 × 23
Take out of the root
∛2,024 = ∛(2³ × 253) = 2∛253
Between cubes
12³ = 1,728 < 2,024 < 2,197 = 13³, so 12 < ∛2,024 < 13 and ∛2,024 ≈ 12.6494

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,8002∛225 ≈ 12.1644
2,00010∛2 ≈ 12.5992
2,007≈ 12.6139
2,0242∛253 ≈ 12.6494
2,19713
2,2002∛275 ≈ 13.0059
2,300≈ 13.2001

FAQ

What is the cube root of 2,024?

∛2,024 = 2∛253 ≈ 12.6494

How to simplify ∛2,024?

Factor 2,024 into primes: 2,024 = 2 × 2 × 2 × 11 × 23. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛2,024 = ∛(2³ × 253) = 2∛253.

Is ∛2,024 a rational number?

No: 2,024 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 ∛2,024 is irrational; its decimal never ends and never repeats: ∛2,024 ≈ 12.6494.

See Also