Chapter 6 - Radical Functions and Rational Exponents - 6-3 Binomial Radical Expressions - Practice and Problem-Solving Exercises - Page 378: 32

$-2$

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{3}+\sqrt{5})(\sqrt{3}-\sqrt{5}) ,$ is equivalent to \begin{align*} & (\sqrt{3})^2-(\sqrt{5})^2 \\&= 3-5 \\&= -2 .\end{align*}