Simplify fourth root of 32

Problem

√(4,32)

Solution

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

√(4,2⋅2⋅2⋅2⋅2)

2. Rewrite the expression using exponents to identify powers that match the index of the radical.

√(4,2)

3. Separate the radicand into a product of a perfect fourth power and the remaining factor.

√(4,2⋅2)

4. Apply the product property of radicals, which states √(n,a⋅b)=√(n,a)⋅√(n,b)

√(4,2)⋅√(4,2)

5. Simplify the radical containing the perfect fourth power.

2⋅√(4,2)

Final Answer

√(4,32)=2√(4,2)

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