Cube Root of 2000

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What is the cube root of 2,000?

Answer

∛2,000 =
10∛2 ≈ 12.5992

Real cube root: the only number whose cube is 2,000.

≈ — rounded to 4 decimal places. 2,000 is not the cube of a rational number, so ∛2,000 is irrational: its decimal expansion never ends and never repeats.

Prime factors
2,000 = (2 × 2 × 2) × 2 × (5 × 5 × 5) = 2⁴ × 5³
Take out of the root
∛2,000 = ∛(2³ × 5³ × 2) = 2 × 5 × ∛2 = 10∛2
Between cubes
12³ = 1,728 < 2,000 < 2,197 = 13³, so 12 < ∛2,000 < 13 and ∛2,000 ≈ 12.5992

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,729≈ 12.0023
1,738≈ 12.0231
1,8002∛225 ≈ 12.1644
2,00010∛2 ≈ 12.5992
2,007≈ 12.6139
2,0242∛253 ≈ 12.6494
2,19713

FAQ

What is the cube root of 2,000?

∛2,000 = 10∛2 ≈ 12.5992

How to simplify ∛2,000?

Factor 2,000 into primes: 2,000 = 2 × 2 × 2 × 2 × 5 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛2,000 = ∛(2³ × 5³ × 2) = 10∛2.

Is ∛2,000 a rational number?

No: 2,000 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 ∛2,000 is irrational; its decimal never ends and never repeats: ∛2,000 ≈ 12.5992.

See Also