Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set - Page 585: 21

$5\sqrt{3x}$

Getting the perfect factors and then extracting its root, the simplified form of the given expression, $ \sqrt{75x} ,$ is \begin{array}{l}\require{cancel} \sqrt{25\cdot3x} \\\\= \sqrt{(5)^2\cdot3x} \\\\= 5\sqrt{3x} .\end{array}