Chapter 10 - Exponents and Radicals - Mid-Chapter Review - Mixed Review - Page 663: 20

$-4$

Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the given expression, $ (\sqrt{5}+3)(\sqrt{5}-3) ,$ is equivalent to \begin{array}{l}\require{cancel} (\sqrt{5}+3)(\sqrt{5}-3) \\\\= (\sqrt{5})^2-(3)^2 \\\\= 5-9 \\\\= -4 .\end{array}