Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 33

$-9-2\sqrt[]{6}$

Using the FOIL method and the properties of radicals, the given expression, $ (\sqrt[]{6}-5)(\sqrt[]{6}+3) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[]{6}(\sqrt[]{6})+\sqrt[]{6}(3)-5(\sqrt[]{6})-5(3) \\\\= 6+3\sqrt[]{6}-5\sqrt[]{6}-15 \\\\= (6-15)+(3\sqrt[]{6}-5\sqrt[]{6}) \\\\= -9-2\sqrt[]{6} .\end{array}