Cube Root of 23328

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What is the cube root of 23,328?

Answer

∛23,328 =
18∛4 ≈ 28.5732

Real cube root: the only number whose cube is 23,328.

≈ — rounded to 4 decimal places. 23,328 is not the cube of a rational number, so ∛23,328 is irrational: its decimal expansion never ends and never repeats.

Prime factors
23,328 = (2 × 2 × 2) × 2 × 2 × (3 × 3 × 3) × (3 × 3 × 3) = 2⁵ × 3⁶
Take out of the root
∛23,328 = ∛(2³ × (3³)² × 4) = 2 × 3² × ∛4 = 18∛4
Between cubes
28³ = 21,952 < 23,328 < 24,389 = 29³, so 28 < ∛23,328 < 29 and ∛23,328 ≈ 28.5732

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
17,57626
19,68327
21,95228
23,32818∛4 ≈ 28.5732
24,38929
27,00030
27,225≈ 30.0831

FAQ

What is the cube root of 23,328?

∛23,328 = 18∛4 ≈ 28.5732

How to simplify ∛23,328?

Factor 23,328 into primes: 23,328 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛23,328 = ∛(2³ × (3³)² × 4) = 18∛4.

Is ∛23,328 a rational number?

No: 23,328 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 ∛23,328 is irrational; its decimal never ends and never repeats: ∛23,328 ≈ 28.5732.

See Also