\sqrt{\sqrt{2}+1}*\sqrt{\sqrt{2}-1}=\sqrt{(\sqrt{2}+1)(\sqrt{2}-1})=\sqrt{(\sqrt{2})^2-1}=\sqrt{2-1}=1
\sqrt{2+\sqrt{3}}*\sqrt{2-\sqrt{3}}=\sqrt{ (2+\sqrt{3})*(2-\sqrt{3})}=\sqrt{2^2-(\sqrt{3})^2}=\sqrt{4-3}=1
\sqrt{\sqrt{7}-\sqrt{3}}*\sqrt{\sqrt{7}+\sqrt{3}}=\sqrt{(\sqrt{7})^2-(\sqrt{3})^2}=\sqrt{7-3}=\sqrt{4}=2
\sqrt{4-2\sqrt{3}}*\sqrt{4+2\sqrt{3}}=\sqrt{4^2-(2\sqrt{3})^2}=\sqrt{16-4*3}=\sqrt{16-12}=\sqrt{4}=2