Evaluate square root of 5* square root of 15

Problem

√(,5)⋅√(,15)

Solution

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

√(,a)⋅√(,b)=√(,a⋅b)

√(,5)⋅√(,15)=√(,5⋅15)

2. Multiply the numbers inside the radical.

5⋅15=75

√(,75)

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

75=25⋅3

√(,25⋅3)

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

√(,25)⋅√(,3)

5√(,3)

Final Answer

√(,5)⋅√(,15)=5√(,3)

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