Cube Root of 67

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Cube root of

What is the cube root of 67?

Answer

∛67 ≈
4.0615

Real cube root: the only number whose cube is 67.

≈ — rounded to 4 decimal places. 67 is not the cube of a rational number, so ∛67 is irrational: its decimal expansion never ends and never repeats.

Prime factors
67 is a prime number: no triple of equal factors.
Between cubes
4³ = 64 < 67 < 125 = 5³, so 4 < ∛67 < 5 and ∛67 ≈ 4.0615

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
644
65≈ 4.0207
66≈ 4.0412
67≈ 4.0615
68≈ 4.0817
69≈ 4.1016
70≈ 4.1213

FAQ

What is the cube root of 67?

∛67 ≈ 4.0615

Can ∛67 be simplified?

No: no prime appears three times in 67, so its only cube factor is 1 and ∛67 is already in simplest form. Since 4³ = 64 < 67 < 125 = 5³, ∛67 lies between 4 and 5: ∛67 ≈ 4.0615.

Is ∛67 a rational number?

No: 67 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 ∛67 is irrational; its decimal never ends and never repeats: ∛67 ≈ 4.0615.

See Also