Cube Root of 60

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Cube root of

What is the cube root of 60?

Answer

∛60 ≈
3.9149

Real cube root: the only number whose cube is 60.

≈ — rounded to 4 decimal places. 60 is not the cube of a rational number, so ∛60 is irrational: its decimal expansion never ends and never repeats.

Prime factors
60 = 2 × 2 × 3 × 5 = 2² × 3 × 5
Take out of the root
No prime appears three times, so ∛60 is already in simplest form.
Between cubes
3³ = 27 < 60 < 64 = 4³, so 3 < ∛60 < 4 and ∛60 ≈ 3.9149

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
57≈ 3.8485
58≈ 3.8709
59≈ 3.893
60≈ 3.9149
61≈ 3.9365
62≈ 3.9579
63≈ 3.9791

FAQ

What is the cube root of 60?

∛60 ≈ 3.9149

Can ∛60 be simplified?

No: no prime appears three times in 60, so its only cube factor is 1 and ∛60 is already in simplest form. Since 3³ = 27 < 60 < 64 = 4³, ∛60 lies between 3 and 4: ∛60 ≈ 3.9149.

Is ∛60 a rational number?

No: 60 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 ∛60 is irrational; its decimal never ends and never repeats: ∛60 ≈ 3.9149.

See Also