Calculate the square root of 96

Problem

√(,96)

Solution

1. Identify the number under the radical and look for its prime factors.

2. Factor the number 96 into its prime components.

96=2⋅48

96=2⋅2⋅24

96=2⋅2⋅2⋅12

96=2⋅2⋅2⋅2⋅6

96=2⋅3

3. Group the factors into perfect squares to simplify the radical.

√(,96)=√(,2⋅2⋅3)

√(,96)=√(,16⋅6)

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

√(,96)=√(,16)⋅√(,6)

5. Simplify the square root of the perfect square.

√(,16)=4

√(,96)=4√(,6)

Final Answer

√(,96)=4√(,6)

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