Evaluate cube root of 189

Problem

√(3,189)

Solution

1. Find the prime factorization of the number under the radical to identify perfect cube factors.

189=3×63

189=3×3×21

189=3×3×3×7

189=3×7

2. Apply the product property of radicals to separate the perfect cube from the remaining factor.

√(3,3×7)=√(3,3)×√(3,7)

3. Simplify the cube root of the perfect cube.

√(3,3)=3

4. Combine the simplified coefficient with the remaining radical.

3×√(3,7)=3√(3,7)

Final Answer

√(3,189)=3√(3,7)

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