Simplify square root of 45p^2

Problem

√(,45*p2)

Solution

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

√(,9⋅5⋅p2)

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

√(,9)⋅√(,p2)⋅√(,5)

3. Evaluate the square roots of the perfect squares.

3⋅|p|⋅√(,5)

4. Combine the terms into the final simplified form.

3*|p|√(,5)

Final Answer

√(,45*p2)=3*|p|√(,5)

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