\sqrt{2} + \sqrt{19} " alt=" \sqrt{6} + \sqrt{15} > \sqrt{2} + \sqrt{19} " align="absmiddle" class="latex-formula">
возведем все в квадрат
(\sqrt{2} + \sqrt{19} )^{2} \\ 6+15+2 \sqrt{90} =21+2* \sqrt{9*10} =21+6 \sqrt{10} =21+ \sqrt{360} \\ \\ 2+19+2 \sqrt{38} =21+2 \sqrt{38} =21+ \sqrt{152} \\ \\ \\ 21+ \sqrt{360}>21+ \sqrt{152} " alt=" (\sqrt{6} + \sqrt{15} )^{2} > (\sqrt{2} + \sqrt{19} )^{2} \\ 6+15+2 \sqrt{90} =21+2* \sqrt{9*10} =21+6 \sqrt{10} =21+ \sqrt{360} \\ \\ 2+19+2 \sqrt{38} =21+2 \sqrt{38} =21+ \sqrt{152} \\ \\ \\ 21+ \sqrt{360}>21+ \sqrt{152} " align="absmiddle" class="latex-formula">