Cube Root of 66

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Cube root of

What is the cube root of 66?

Answer

∛66 ≈
4.0412

Real cube root: the only number whose cube is 66.

≈ — rounded to 4 decimal places. 66 is not the cube of a rational number, so ∛66 is irrational: its decimal expansion never ends and never repeats.

Prime factors
66 = 2 × 3 × 11
Take out of the root
No prime appears three times, so ∛66 is already in simplest form.
Between cubes
4³ = 64 < 66 < 125 = 5³, so 4 < ∛66 < 5 and ∛66 ≈ 4.0412

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
63≈ 3.9791
644
65≈ 4.0207
66≈ 4.0412
67≈ 4.0615
68≈ 4.0817
69≈ 4.1016

FAQ

What is the cube root of 66?

∛66 ≈ 4.0412

Can ∛66 be simplified?

No: no prime appears three times in 66, so its only cube factor is 1 and ∛66 is already in simplest form. Since 4³ = 64 < 66 < 125 = 5³, ∛66 lies between 4 and 5: ∛66 ≈ 4.0412.

Is ∛66 a rational number?

No: 66 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 ∛66 is irrational; its decimal never ends and never repeats: ∛66 ≈ 4.0412.

See Also