Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 39

$15$

Using $(a+b)(a-b)=a^2-b^2$, or the special product of the sum and difference of like terms, the given expression, $ (3\sqrt{2}-\sqrt{3})(3\sqrt{2}+\sqrt{3}) ,$ simplifies to \begin{array}{l}\require{cancel} (3\sqrt{2})^2-(\sqrt{3})^2 \\\\= 9(2)-3 \\\\= 18-3 \\\\= 15 .\end{array}