Evaluate square root of 6* square root of 2

Problem

√(,6)⋅√(,2)

Solution

1. Apply the product property of radicals, which states that √(,a)⋅√(,b)=√(,a⋅b) for non-negative numbers.

√(,6)⋅√(,2)=√(,6⋅2)

2. Multiply the numbers inside the radical.

√(,6⋅2)=√(,12)

3. Factor the number inside the radical to find the largest perfect square factor.

√(,12)=√(,4⋅3)

4. Simplify the radical by taking the square root of the perfect square factor.

√(,4⋅3)=2√(,3)

Final Answer

√(,6)⋅√(,2)=2√(,3)

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