Cube Root of 189

Cube Root Calculator
Cube root of

What is the cube root of 189?

Answer

∛189 =
3∛7 ≈ 5.7388

Real cube root: the only number whose cube is 189.

≈ — rounded to 4 decimal places. 189 is not the cube of a rational number, so ∛189 is irrational: its decimal expansion never ends and never repeats.

Prime factors
189 = (3 × 3 × 3) × 7 = 3³ × 7
Take out of the root
∛189 = ∛(3³ × 7) = 3∛7
Between cubes
5³ = 125 < 189 < 216 = 6³, so 5 < ∛189 < 6 and ∛189 ≈ 5.7388

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
180≈ 5.6462
182≈ 5.6671
187≈ 5.7185
1893∛7 ≈ 5.7388
1924∛3 ≈ 5.769
196≈ 5.8088
197≈ 5.8186

FAQ

What is the cube root of 189?

∛189 = 3∛7 ≈ 5.7388

How to simplify ∛189?

Factor 189 into primes: 189 = 3 × 3 × 3 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛189 = ∛(3³ × 7) = 3∛7.

Is ∛189 a rational number?

No: 189 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 ∛189 is irrational; its decimal never ends and never repeats: ∛189 ≈ 5.7388.

See Also