Cube Root of 32

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Cube root of

What is the cube root of 32?

Answer

∛32 =
2∛4 ≈ 3.1748

Real cube root: the only number whose cube is 32.

≈ — rounded to 4 decimal places. 32 is not the cube of a rational number, so ∛32 is irrational: its decimal expansion never ends and never repeats.

Prime factors
32 = (2 × 2 × 2) × 2 × 2 = 2⁵
Take out of the root
∛32 = ∛(2³ × 4) = 2∛4
Between cubes
3³ = 27 < 32 < 64 = 4³, so 3 < ∛32 < 4 and ∛32 ≈ 3.1748

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
29.5≈ 3.0899
30≈ 3.1072
31≈ 3.1414
322∛4 ≈ 3.1748
32.7683.2
33≈ 3.2075
34≈ 3.2396

FAQ

What is the cube root of 32?

∛32 = 2∛4 ≈ 3.1748

How to simplify ∛32?

Factor 32 into primes: 32 = 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: ∛32 = ∛(2³ × 4) = 2∛4.

Is ∛32 a rational number?

No: 32 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 ∛32 is irrational; its decimal never ends and never repeats: ∛32 ≈ 3.1748.

See Also