Simplify cube root of 135

Problem

√(3,135)

Solution

1. Find the prime factorization of the radicand by dividing by small prime numbers.

135=3⋅45

135=3⋅3⋅15

135=3⋅3⋅3⋅5

135=3⋅5

2. Rewrite the radical using the prime factorization found in the previous step.

√(3,135)=√(3,3⋅5)

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

√(3,3⋅5)=√(3,3)⋅√(3,5)

4. Simplify the perfect cube by taking the cube root of 3

√(3,3)⋅√(3,5)=3⋅√(3,5)

Final Answer

√(3,135)=3√(3,5)

Want more problems? Check here!