Cube Root of 119

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Cube root of

What is the cube root of 119?

Answer

∛119 ≈
4.9187

Real cube root: the only number whose cube is 119.

≈ — rounded to 4 decimal places. 119 is not the cube of a rational number, so ∛119 is irrational: its decimal expansion never ends and never repeats.

Prime factors
119 = 7 × 17
Take out of the root
No prime appears three times, so ∛119 is already in simplest form.
Between cubes
4³ = 64 < 119 < 125 = 5³, so 4 < ∛119 < 5 and ∛119 ≈ 4.9187

See Also

FAQ

What is the cube root of 119?

∛119 ≈ 4.9187

Can ∛119 be simplified?

No: no prime appears three times in 119, so its only cube factor is 1 and ∛119 is already in simplest form. Since 4³ = 64 < 119 < 125 = 5³, ∛119 lies between 4 and 5: ∛119 ≈ 4.9187.

Is ∛119 a rational number?

No: 119 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 ∛119 is irrational; its decimal never ends and never repeats: ∛119 ≈ 4.9187.