Simplify square root of 512x^2

Problem

√(,512*x2)

Solution

1. Factor the radicand into a perfect square and a non-perfect square.

√(,256⋅2⋅x2)

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

√(,256)⋅√(,x2)⋅√(,2)

3. Evaluate the square roots of the perfect squares.

16⋅|x|⋅√(,2)

4. Combine the terms into the final simplified form.

16*|x|√(,2)

Final Answer

√(,512*x2)=16*|x|√(,2)

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