Witaj :)
[tex](\sqrt{3-\sqrt{5} } +\sqrt{\sqrt{5+3} } )^2=(\sqrt{3-\sqrt{5}}+\sqrt{\sqrt{8} })^2=\\\\=(\sqrt{3-\sqrt{5} }+\sqrt[4]{8} )^2=(\sqrt{3-\sqrt{5} })^2+2\cdot \sqrt{3-\sqrt{5} }\cdot \sqrt[4]{8} +(\sqrt[4]{8})^2=\\\\=3-\sqrt{5} +2\sqrt{3-\sqrt{5} }\cdot\sqrt[4]{8}+\sqrt{8} =\\\\=3-\sqrt{5}+2\sqrt[2\cdot2]{(3-\sqrt{5} )^2} \cdot \sqrt[4]{8}+2\sqrt{\\2}=\\\\=3-\sqrt{5}+2\sqrt[4]{9-6\sqrt{5}+5 } \cdot \sqrt[4]{8}+2 \sqrt{2} =\\\\=3-\sqrt{5}+2\sqrt[4]{(14-6\sqrt{5} )\cdot 8} +2\sqrt{2}=\\\\[/tex]
[tex]=3-\sqrt{5} +2\sqrt[4]{112-48\sqrt{5} } +2\sqrt{2}=\\\\=3-\sqrt{5}+2\sqrt[4]{16(7-3\sqrt{5}) } +2\sqrt{2}=\\\\=3-\sqrt{5}+4\sqrt[4]{7-3\sqrt{5} } +2\sqrt{2}[/tex]
[tex]ODP.:\ (\sqrt{3-\sqrt{5}}+\sqrt{\sqrt{5+3} } )^2= \boxed {3-\sqrt{5}+4\sqrt[4]{7-3\sqrt{5} }+2\sqrt{2} }[/tex]
