Evaluate cube root of 48

Problem

√(3,48)

Solution

1. Factor the number inside the radical into its prime factors.

√(3,48)=√(3,2⋅2⋅2⋅2⋅3)

2. Group the factors into sets of three, as we are looking for the cube root.

√(3,48)=√(3,2⋅2⋅3)

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

√(3,48)=√(3,2)⋅√(3,2⋅3)

4. Simplify the radical by taking the cube root of the perfect cube and multiplying the remaining factors.

√(3,48)=2⋅√(3,6)

Final Answer

√(3,48)=2√(3,6)

Want more problems? Check here!