Cube Root of 68

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Cube root of

What is the cube root of 68?

Answer

∛68 ≈
4.0817

Real cube root: the only number whose cube is 68.

≈ — rounded to 4 decimal places. 68 is not the cube of a rational number, so ∛68 is irrational: its decimal expansion never ends and never repeats.

Prime factors
68 = 2 × 2 × 17 = 2² × 17
Take out of the root
No prime appears three times, so ∛68 is already in simplest form.
Between cubes
4³ = 64 < 68 < 125 = 5³, so 4 < ∛68 < 5 and ∛68 ≈ 4.0817

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
65≈ 4.0207
66≈ 4.0412
67≈ 4.0615
68≈ 4.0817
69≈ 4.1016
70≈ 4.1213
71≈ 4.1408

FAQ

What is the cube root of 68?

∛68 ≈ 4.0817

Can ∛68 be simplified?

No: no prime appears three times in 68, so its only cube factor is 1 and ∛68 is already in simplest form. Since 4³ = 64 < 68 < 125 = 5³, ∛68 lies between 4 and 5: ∛68 ≈ 4.0817.

Is ∛68 a rational number?

No: 68 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 ∛68 is irrational; its decimal never ends and never repeats: ∛68 ≈ 4.0817.

See Also