Evaluate square root of 5* square root of 10

Problem

√(,5)⋅√(,10)

Solution

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

√(,5)⋅√(,10)=√(,5⋅10)

2. Multiply the numbers inside the square root.

√(,5⋅10)=√(,50)

3. Factor the radicand to find the largest perfect square factor.

√(,50)=√(,25⋅2)

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

√(,25⋅2)=5√(,2)

Final Answer

√(,5)⋅√(,10)=5√(,2)

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