Cube Root of 2007

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What is the cube root of 2,007?

Answer

∛2,007 ≈
12.6139

Real cube root: the only number whose cube is 2,007.

≈ — rounded to 4 decimal places. 2,007 is not the cube of a rational number, so ∛2,007 is irrational: its decimal expansion never ends and never repeats.

Prime factors
2,007 = 3 × 3 × 223 = 3² × 223
Take out of the root
No prime appears three times, so ∛2,007 is already in simplest form.
Between cubes
12³ = 1,728 < 2,007 < 2,197 = 13³, so 12 < ∛2,007 < 13 and ∛2,007 ≈ 12.6139

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
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
2,2002∛275 ≈ 13.0059

FAQ

What is the cube root of 2,007?

∛2,007 ≈ 12.6139

Can ∛2,007 be simplified?

No: no prime appears three times in 2,007, so its only cube factor is 1 and ∛2,007 is already in simplest form. Since 12³ = 1,728 < 2,007 < 2,197 = 13³, ∛2,007 lies between 12 and 13: ∛2,007 ≈ 12.6139.

Is ∛2,007 a rational number?

No: 2,007 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 ∛2,007 is irrational; its decimal never ends and never repeats: ∛2,007 ≈ 12.6139.

See Also