Simplify square root of 512k^2

Problem

√(,512*k2)

Solution

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

512=256⋅2

2. Rewrite the square root using the product property of radicals.

√(,256⋅2⋅k2)

3. Separate the terms into individual square roots.

√(,256)⋅√(,k2)⋅√(,2)

4. Evaluate the square roots of the perfect squares.

16⋅|k|⋅√(,2)

5. Combine the terms into the final simplified form.

16*|k|√(,2)

Final Answer

√(,512*k2)=16*|k|√(,2)

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