Cube Root of 123

Cube Root Calculator
Cube root of

What is the cube root of 123?

Answer

∛123 ≈
4.9732

Real cube root: the only number whose cube is 123.

≈ — rounded to 4 decimal places. 123 is not the cube of a rational number, so ∛123 is irrational: its decimal expansion never ends and never repeats.

Prime factors
123 = 3 × 41
Take out of the root
No prime appears three times, so ∛123 is already in simplest form.
Between cubes
4³ = 64 < 123 < 125 = 5³, so 4 < ∛123 < 5 and ∛123 ≈ 4.9732

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1202∛15 ≈ 4.9324
121≈ 4.9461
122≈ 4.9597
123≈ 4.9732
124≈ 4.9866
1255
126≈ 5.0133

FAQ

What is the cube root of 123?

∛123 ≈ 4.9732

Can ∛123 be simplified?

No: no prime appears three times in 123, so its only cube factor is 1 and ∛123 is already in simplest form. Since 4³ = 64 < 123 < 125 = 5³, ∛123 lies between 4 and 5: ∛123 ≈ 4.9732.

Is ∛123 a rational number?

No: 123 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 ∛123 is irrational; its decimal never ends and never repeats: ∛123 ≈ 4.9732.

See Also