Simplify the expression. (Assume that all variables are positive.) \[ \sqrt{\frac{121 x^{3}}{49 x}} \]

To simplify the expression \(\sqrt{\frac{121 x^{3}}{49 x}}\), we start by simplifying the fraction inside the square root: \[ \frac{121 x^{3}}{49 x} = \frac{121}{49} \cdot \frac{x^{3}}{x} \] Since \( \frac{x^{3}}{x} = x^{2} \), we can rewrite the expression as: \[ \frac{121}{49} \cdot x^{2} \] Now, substituting that back into the square root gives us: \[ \sqrt{\frac{121}{49} \cdot x^{2}} = \sqrt{\frac{121}{49}} \cdot \sqrt{x^{2}} \] Now we can simplify each part: 1. \(\sqrt{\frac{121}{49}} = \frac{\sqrt{121}}{\sqrt{49}} = \frac{11}{7}\) 2. \(\sqrt{x^{2}} = x\) Putting it all together, we have: \[ \sqrt{\frac{121 x^{3}}{49 x}} = \frac{11}{7} \cdot x \] Thus, the simplified expression is: \[ \frac{11x}{7} \]