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.)

We start with the expression \[ \sqrt{\frac{x^2 y}{225}} \] and apply the quotient rule for square roots, which states that \[ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}, \] for \( a, b > 0 \). Thus, we have \[ \sqrt{\frac{x^2 y}{225}} = \frac{\sqrt{x^2 y}}{\sqrt{225}}. \] Next, compute the denominator: \[ \sqrt{225} = 15. \] Now, simplify the numerator. Since \( x \) is positive, we know that \[ \sqrt{x^2} = x. \] Thus, \[ \sqrt{x^2 y} = \sqrt{x^2} \sqrt{y} = x \sqrt{y}. \] Putting these together, our expression becomes: \[ \frac{x \sqrt{y}}{15}. \] This is the simplified form of the original expression.