Evaluate square root of 18 square root of 45/10

Problem

√(,18)⋅√(,45/10)

Solution

1. Simplify the fraction inside the second square root by dividing the numerator and denominator by their greatest common divisor, 5.

45/10=9/2

2. Combine the square roots using the property √(,a)⋅√(,b)=√(,a⋅b)

√(,18)⋅√(,9/2)=√(,18⋅9/2)

3. Multiply the terms inside the square root.

18⋅9/2=9⋅9

9⋅9=81

4. Evaluate the square root of the resulting product.

√(,81)=9

Final Answer

√(,18)⋅√(,45/10)=9

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