Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set - Page 585: 40

$2x^4\sqrt{6}$

Getting the perfect factors and then extracting its root, the simplified form of the given expression, $ \sqrt{24x^{8}} ,$ is \begin{array}{l}\require{cancel} \sqrt{4x^8\cdot6} \\\\= \sqrt{(2x^4)^2\cdot6} \\\\= 2x^4\sqrt{6} .\end{array}