Evaluate square root of 6* square root of 8

Problem

√(,6)⋅√(,8)

Solution

1. Apply the product property of radicals to combine the two square roots into a single radical.

√(,a)⋅√(,b)=√(,a⋅b)

2. Multiply the numbers inside the radical.

√(,6⋅8)=√(,48)

3. Identify the largest perfect square factor of 48 to simplify the expression.

48=16⋅3

4. Apply the product property in reverse to separate the perfect square.

√(,16⋅3)=√(,16)⋅√(,3)

5. Evaluate the square root of the perfect square.

√(,16)=4

Final Answer

√(,6)⋅√(,8)=4√(,3)

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