[tex](\sqrt{3-\sqrt5}+\sqrt{\sqrt5+3})^2=\\\\(\sqrt{3-\sqrt5}+\sqrt{3+\sqrt5})^2=\\\\(\sqrt{3-\sqrt5})^2+2\cdot\sqrt{3-\sqrt5}\cdot\sqrt{3+\sqrt5}+(\sqrt{3+\sqrt5})^2=\\\\3-\sqrt5+2\cdot\sqrt{(3-\sqrt5)\cdot(3-\sqrt5)}+3+\sqrt5=\\\\6+2\cdot\sqrt{9-5}=6+2\cdot\sqrt4=6+2\cdot2=6+4=10\\[/tex]
