Simplify cube root of 16x^5

Problem

√(3,16*x5)

Solution

1. Factor the radicand into perfect cubes and remaining factors.

√(3,2⋅x5)

√(3,2⋅2⋅x3⋅x2)

2. Group the perfect cube terms together.

√(3,(2⋅x3)⋅(2⋅x2))

3. Apply the product property of radicals √(n,a*b)=√(n,a)⋅√(n,b)

√(3,2⋅x3)⋅√(3,2⋅x2)

4. Simplify the cube root of the perfect cubes.

2*x⋅√(3,2*x2)

Final Answer

√(3,16*x5)=2*x√(3,2*x2)

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