Chapter 9 - Roots and Radicals - 9.1 - Roots and Radicals - Problem Set 9.1 - Page 401: 81

$\approx2.1$

Using the properties of radicals, a rational approximation (to the nearest tenth) of the given expression, $ 9\sqrt{6}-3\sqrt{5}+2\sqrt{6}-7\sqrt{5}-\sqrt{6} ,$ is \begin{array}{l}\require{cancel} (9\sqrt{6}+2\sqrt{6}-\sqrt{6})+(-3\sqrt{5}-7\sqrt{5}) \\\\= 10\sqrt{6}-10\sqrt{5} \\\\ \approx24.5-22.4 \\\\ \approx2.1 .\end{array}