Cube Root of 128

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Cube root of

What is the cube root of 128?

Answer

∛128 =
4∛2 ≈ 5.0397

Real cube root: the only number whose cube is 128.

≈ — rounded to 4 decimal places. 128 is not the cube of a rational number, so ∛128 is irrational: its decimal expansion never ends and never repeats.

Prime factors
128 = (2 × 2 × 2) × (2 × 2 × 2) × 2 = 2⁷
Take out of the root
∛128 = ∛((2³)² × 2) = 2² × ∛2 = 4∛2
Between cubes
5³ = 125 < 128 < 216 = 6³, so 5 < ∛128 < 6 and ∛128 ≈ 5.0397

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1255
126≈ 5.0133
127≈ 5.0265
1284∛2 ≈ 5.0397
129≈ 5.0528
131≈ 5.0788
132≈ 5.0916

FAQ

What is the cube root of 128?

∛128 = 4∛2 ≈ 5.0397

How to simplify ∛128?

Factor 128 into primes: 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛128 = ∛((2³)² × 2) = 4∛2.

Is ∛128 a rational number?

No: 128 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 ∛128 is irrational; its decimal never ends and never repeats: ∛128 ≈ 5.0397.

See Also