Rationalize the denominator. Assume that all variables represent positive real numbers. \( \sqrt{\frac{121}{x}} \) \( \sqrt{\frac{121}{x}}=\square \) (Type an exact answer, using radicals as needed.)

To rationalize the denominator of \( \sqrt{\frac{121}{x}} \), start by rewriting the expression as \( \frac{\sqrt{121}}{\sqrt{x}} \). Since \( \sqrt{121} = 11 \), this simplifies to \( \frac{11}{\sqrt{x}} \). To rationalize the denominator, multiply both the numerator and the denominator by \( \sqrt{x} \): \[ \frac{11}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}} = \frac{11\sqrt{x}}{x} \] So, \( \sqrt{\frac{121}{x}} = \frac{11\sqrt{x}}{x} \). Therefore, the final answer is: \[ \frac{11\sqrt{x}}{x} \]