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What is the cube root of 1,729?

Answer

∛1,729 ≈
12.0023

Real cube root: the only number whose cube is 1,729.

≈ — rounded to 4 decimal places. 1,729 is not the cube of a rational number, so ∛1,729 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,729 = 7 × 13 × 19
Take out of the root
No prime appears three times, so ∛1,729 is already in simplest form.
Between cubes
12³ = 1,728 < 1,729 < 2,197 = 13³, so 12 < ∛1,729 < 13 and ∛1,729 ≈ 12.0023

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,725≈ 11.9931
1,726≈ 11.9954
1,72812
1,729≈ 12.0023
1,738≈ 12.0231
1,8002∛225 ≈ 12.1644
2,00010∛2 ≈ 12.5992

FAQ

What is the cube root of 1,729?

∛1,729 ≈ 12.0023

Can ∛1,729 be simplified?

No: no prime appears three times in 1,729, so its only cube factor is 1 and ∛1,729 is already in simplest form. Since 12³ = 1,728 < 1,729 < 2,197 = 13³, ∛1,729 lies between 12 and 13: ∛1,729 ≈ 12.0023.

Is ∛1,729 a rational number?

No: 1,729 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 ∛1,729 is irrational; its decimal never ends and never repeats: ∛1,729 ≈ 12.0023.

See Also