Cube Root of 432

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Cube root of

What is the cube root of 432?

Answer

∛432 =
6∛2 ≈ 7.5595

Real cube root: the only number whose cube is 432.

≈ — rounded to 4 decimal places. 432 is not the cube of a rational number, so ∛432 is irrational: its decimal expansion never ends and never repeats.

Prime factors
432 = (2 × 2 × 2) × 2 × (3 × 3 × 3) = 2⁴ × 3³
Take out of the root
∛432 = ∛(2³ × 3³ × 2) = 2 × 3 × ∛2 = 6∛2
Between cubes
7³ = 343 < 432 < 512 = 8³, so 7 < ∛432 < 8 and ∛432 ≈ 7.5595

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Recalculate with different values ↑

Cube roots of nearby values

N∛N
3437
3755∛3 ≈ 7.2112
425≈ 7.5185
4326∛2 ≈ 7.5595
445≈ 7.6346
4484∛7 ≈ 7.6517
450≈ 7.6631

FAQ

What is the cube root of 432?

∛432 = 6∛2 ≈ 7.5595

How to simplify ∛432?

Factor 432 into primes: 432 = 2 × 2 × 2 × 2 × 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: ∛432 = ∛(2³ × 3³ × 2) = 6∛2.

Is ∛432 a rational number?

No: 432 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 ∛432 is irrational; its decimal never ends and never repeats: ∛432 ≈ 7.5595.

See Also