Cube Root of 65

Cube Root Calculator
Cube root of

What is the cube root of 65?

Answer

∛65 ≈
4.0207

Real cube root: the only number whose cube is 65.

≈ — rounded to 4 decimal places. 65 is not the cube of a rational number, so ∛65 is irrational: its decimal expansion never ends and never repeats.

Prime factors
65 = 5 × 13
Take out of the root
No prime appears three times, so ∛65 is already in simplest form.
Between cubes
4³ = 64 < 65 < 125 = 5³, so 4 < ∛65 < 5 and ∛65 ≈ 4.0207

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
62≈ 3.9579
63≈ 3.9791
644
65≈ 4.0207
66≈ 4.0412
67≈ 4.0615
68≈ 4.0817

FAQ

What is the cube root of 65?

∛65 ≈ 4.0207

Can ∛65 be simplified?

No: no prime appears three times in 65, so its only cube factor is 1 and ∛65 is already in simplest form. Since 4³ = 64 < 65 < 125 = 5³, ∛65 lies between 4 and 5: ∛65 ≈ 4.0207.

Is ∛65 a rational number?

No: 65 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 ∛65 is irrational; its decimal never ends and never repeats: ∛65 ≈ 4.0207.

See Also