Use the quotient rule to simplify. Assume that all variables represent positive real numbers. \( \sqrt{\frac{x^{2} y}{225}} \) \( \sqrt{\frac{x^{2} y}{225}}=\square \) (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.)

To simplify \( \sqrt{\frac{x^{2} y}{225}} \), we can apply the property of square roots that states \( \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \). So, we rewrite it as: \[ \sqrt{\frac{x^{2} y}{225}} = \frac{\sqrt{x^{2} y}}{\sqrt{225}}. \] Now, we simplify each part: - \( \sqrt{225} = 15 \). - \( \sqrt{x^2 y} = \sqrt{x^2} \cdot \sqrt{y} = x \sqrt{y} \) since \( x \) is positive. Combining these, we have: \[ \frac{x \sqrt{y}}{15}. \] Thus, the simplified form is \[ \frac{x \sqrt{y}}{15}. \]