Cube Root of 126

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Cube root of

What is the cube root of 126?

Answer

∛126 ≈
5.0133

Real cube root: the only number whose cube is 126.

≈ — rounded to 4 decimal places. 126 is not the cube of a rational number, so ∛126 is irrational: its decimal expansion never ends and never repeats.

Prime factors
126 = 2 × 3 × 3 × 7 = 2 × 3² × 7
Take out of the root
No prime appears three times, so ∛126 is already in simplest form.
Between cubes
5³ = 125 < 126 < 216 = 6³, so 5 < ∛126 < 6 and ∛126 ≈ 5.0133

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
123≈ 4.9732
124≈ 4.9866
1255
126≈ 5.0133
127≈ 5.0265
1284∛2 ≈ 5.0397
129≈ 5.0528

FAQ

What is the cube root of 126?

∛126 ≈ 5.0133

Can ∛126 be simplified?

No: no prime appears three times in 126, so its only cube factor is 1 and ∛126 is already in simplest form. Since 5³ = 125 < 126 < 216 = 6³, ∛126 lies between 5 and 6: ∛126 ≈ 5.0133.

Is ∛126 a rational number?

No: 126 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 ∛126 is irrational; its decimal never ends and never repeats: ∛126 ≈ 5.0133.

See Also