Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set - Page 585: 14

$\sqrt{x}$

Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $ \sqrt{\dfrac{5x}{11}}\cdot\sqrt{\dfrac{11}{5}} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{\dfrac{5x}{11}\cdot\dfrac{11}{5}} \\\\= \sqrt{\dfrac{\cancel{5}x}{\cancel{11}}\cdot\dfrac{\cancel{11}}{\cancel{5}}} \\\\= \sqrt{x} .\end{array}