Evaluate square root of 10* square root of 15

Problem

√(,10)⋅√(,15)

Solution

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

√(,a)⋅√(,b)=√(,a⋅b)

2. Multiply the numbers inside the radical.

√(,10⋅15)=√(,150)

3. Find the largest perfect square factor of 150 to simplify the radical.

150=25⋅6

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

√(,25⋅6)=√(,25)⋅√(,6)

5. Calculate the square root of 25.

5⋅√(,6)=5√(,6)

Final Answer

√(,10)⋅√(,15)=5√(,6)

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