Evaluate fourth root of 96

Problem

√(4,96)

Solution

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

96=2⋅48

96=2⋅2⋅24

96=2⋅2⋅2⋅12

96=2⋅2⋅2⋅2⋅6

96=2⋅3

2. Rewrite the expression by grouping the factors into powers of four to match the index of the root.

√(4,96)=√(4,2⋅2⋅3)

√(4,96)=√(4,2⋅6)

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

√(4,96)=√(4,2)⋅√(4,6)

4. Simplify the radical by evaluating the fourth root of the perfect fourth power.

√(4,2)=2

√(4,96)=2√(4,6)

Final Answer

√(4,96)=2√(4,6)

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