Simplify square root of 75x^2y

Problem

√(,75*x2*y)

Solution

1. Factor the radicand into its prime factors and perfect squares.

√(,25⋅3⋅x2⋅y)

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

√(,25)⋅√(,x2)⋅√(,3*y)

3. Simplify the square roots of the perfect squares.

5⋅|x|⋅√(,3*y)

4. Combine the terms outside the radical.

5*|x|√(,3*y)

Final Answer

√(,75*x2*y)=5*|x|√(,3*y)

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