Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 54

$8-2\sqrt{15}$

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, and the properties of radicals, the given expression, $ (\sqrt{5}-\sqrt{3})^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (\sqrt{5})^2+2(\sqrt{5})(-\sqrt{3})+(-\sqrt{3})^2 \\\\= 5-2\sqrt{15}+3 \\\\= 8-2\sqrt{15} .\end{array}