Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 31

$56+15\sqrt[]{2}$

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $ (\sqrt[]{2}+6)(\sqrt[]{2}+9) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[]{2}(\sqrt[]{2})+\sqrt[]{2}(9)+6(\sqrt[]{2})+6(9) \\\\= 2+9\sqrt[]{2}+6\sqrt[]{2}+54 \\\\= (2+54)+(9\sqrt[]{2}+6\sqrt[]{2}) \\\\= 56+15\sqrt[]{2} .\end{array}