Chapter 9 - Roots and Radicals - 9.1 - Roots and Radicals - Problem Set 9.1 - Page 401: 82

$\approx10.1$

Using the properties of radicals, a rational approximation (to the nearest tenth) of the given expression, $ 8\sqrt{7}-2\sqrt{10}+4\sqrt{7}-3\sqrt{10}-7\sqrt{7}+4\sqrt{10} ,$ is \begin{array}{l}\require{cancel} (8\sqrt{7}+4\sqrt{7}-7\sqrt{7})+(-2\sqrt{10}-3\sqrt{10}+4\sqrt{10}) \\\\= 5\sqrt{7}-\sqrt{10} \\\\ \approx13.22876-3.1623 \\\\ \approx10.1 .\end{array}