Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 53

$5-2\sqrt{6}$

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, and the properties of radicals, the given expression, $ (\sqrt{3}-\sqrt{2})^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (\sqrt{3})^2+2(\sqrt{3})(-\sqrt{2})+(-\sqrt{2})^2 \\\\= 3-2\sqrt{6}+2 \\\\= 5-2\sqrt{6} .\end{array}