a)
(\sqrt{3+\sqrt5}+\sqrt{3-\sqrt5)}^2=(\sqrt{3+\sqrt5)}^2+2*(\sqrt{3+\sqrt5}*\sqrt{3-\sqrt5})+(\sqrt{3-\sqrt5)}^2=3+\sqrt5*2*\sqrt{(3+\sqrt5)(3-\sqrt5}+3-\sqrt5=6+2*\sqrt{3^2-(\sqrt5)^2}=
6+2*\sqrt{9-5}=6+2*\sqrt4=6+2*2=10
b)
(\sqrt{2-\sqrt3}-\sqrt{2+\sqrt3})^2=(\sqrt{2-\sqrt3)}^2-2*(\sqrt{2-\sqrt3}*\sqrt{2+\sqrt3})+(\sqrt{2+\sqrt3)}^2=
2-\sqrt3*2-2*\sqrt{(2-\sqrt3)(2+\sqrt3)}+2+\sqrt3=4-2*\sqrt{2^2-(\sqrt3)^2}=4-2*\sqrt{4-3}=4-2*\sqrt1=4-2=2