1. The problem is to simplify or work with an expression involving the square root of the product $x \cdot y$, not just the product $x y$. 2. The square root of a product rule states: $$\sqrt{x y} = \sqrt{x} \cdot \sqrt{y}$$ This means the square root of a product is the product of the square roots. 3. Important rules: - Both $x$ and $y$ should be non-negative if we are working with real numbers to keep the square root defined. - You cannot simplify $\sqrt{x y}$ as $x y$; they are different. 4. Example: If you have $\sqrt{x y}$, you can write it as $\sqrt{x} \times \sqrt{y}$. 5. If you want to solve or simplify an equation involving $\sqrt{x y}$, always treat it as the square root of the product, not the product itself. Final answer: The expression $\sqrt{x y}$ means the square root of the product of $x$ and $y$, which equals $\sqrt{x} \cdot \sqrt{y}$, not $x y$.