Simplify fourth root of 96

Problem

√(4,96)

Solution

1. Factor the radicand 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 to isolate the largest perfect fourth power.

√(4,2⋅3)=√(4,2⋅2⋅3)

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

√(4,2)⋅√(4,2⋅3)

4. Simplify the fourth root of the perfect fourth power and multiply the remaining factors.

2⋅√(4,6)

Final Answer

√(4,96)=2√(4,6)

Want more problems? Check here!