[tex]\sqrt{10+\sqrt{24}+\sqrt{40}+\sqrt{60}}-\sqrt{8+2\sqrt{15}}=\sqrt{2+3+5+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}-\sqrt{5+2\sqrt{15}+3}[/tex]
[tex]=\sqrt{(\sqrt{2}+\sqrt{3}+\sqrt{5})^2}-\sqrt{(\sqrt{5}+\sqrt{3})^2} =\sqrt{2}+\sqrt{3}+\sqrt{5}-\sqrt{5}-\sqrt{3}=\sqrt{2}[/tex]