Evaluate cube root of 135

Problem

√(3,135)

Solution

1. Identify the prime factorization of the number inside the radical.

135=5×27

2. Recognize that 27 is a perfect cube.

27=3

3. Rewrite the expression using the prime factors.

√(3,135)=√(3,3×5)

4. Apply the property of radicals √(n,a×b)=√(n,a)×√(n,b) to separate the perfect cube.

√(3,3×5)=√(3,3)×√(3,5)

5. Simplify the cube root of the perfect cube.

√(3,3)=3

Final Answer

√(3,135)=3√(3,5)

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