Cube Root of 192

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Cube root of

What is the cube root of 192?

Answer

∛192 =
4∛3 ≈ 5.769

Real cube root: the only number whose cube is 192.

≈ — rounded to 4 decimal places. 192 is not the cube of a rational number, so ∛192 is irrational: its decimal expansion never ends and never repeats.

Prime factors
192 = (2 × 2 × 2) × (2 × 2 × 2) × 3 = 2⁶ × 3
Take out of the root
∛192 = ∛((2³)² × 3) = 2² × ∛3 = 4∛3
Between cubes
5³ = 125 < 192 < 216 = 6³, so 5 < ∛192 < 6 and ∛192 ≈ 5.769

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
182≈ 5.6671
187≈ 5.7185
1893∛7 ≈ 5.7388
1924∛3 ≈ 5.769
196≈ 5.8088
197≈ 5.8186
2002∛25 ≈ 5.848

FAQ

What is the cube root of 192?

∛192 = 4∛3 ≈ 5.769

How to simplify ∛192?

Factor 192 into primes: 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛192 = ∛((2³)² × 3) = 4∛3.

Is ∛192 a rational number?

No: 192 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 ∛192 is irrational; its decimal never ends and never repeats: ∛192 ≈ 5.769.

See Also