Evaluate fourth root of 32

Problem

√(4,32)

Solution

1. Rewrite the number inside the radical as a product of its prime factors.

√(4,2⋅2⋅2⋅2⋅2)

2. Group the factors into a power that matches the index of the root.

√(4,2⋅2)

3. Apply the property of radicals √(n,a⋅b)=√(n,a)⋅√(n,b) to separate the terms.

√(4,2)⋅√(4,2)

4. Simplify the first term by evaluating the fourth root of the fourth power.

2⋅√(4,2)

Final Answer

√(4,32)=2√(4,2)

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