Cube Root of 99

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Cube root of

What is the cube root of 99?

Answer

∛99 ≈
4.6261

Real cube root: the only number whose cube is 99.

≈ — rounded to 4 decimal places. 99 is not the cube of a rational number, so ∛99 is irrational: its decimal expansion never ends and never repeats.

Prime factors
99 = 3 × 3 × 11 = 3² × 11
Take out of the root
No prime appears three times, so ∛99 is already in simplest form.
Between cubes
4³ = 64 < 99 < 125 = 5³, so 4 < ∛99 < 5 and ∛99 ≈ 4.6261

See Also

FAQ

What is the cube root of 99?

∛99 ≈ 4.6261

Can ∛99 be simplified?

No: no prime appears three times in 99, so its only cube factor is 1 and ∛99 is already in simplest form. Since 4³ = 64 < 99 < 125 = 5³, ∛99 lies between 4 and 5: ∛99 ≈ 4.6261.

Is ∛99 a rational number?

No: 99 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 ∛99 is irrational; its decimal never ends and never repeats: ∛99 ≈ 4.6261.