Verified answer

Ответ:

[tex]2[/tex]

Объяснение:

[tex]\sqrt[4]{8+\sqrt{60}}*\sqrt{\sqrt{5}+\sqrt{3}}*( \sqrt{5}-\sqrt{3})=\\\\=\sqrt[4]{8+\sqrt{4*15}}*\sqrt{\sqrt{5}+\sqrt{3}}*( \sqrt{5}-\sqrt{3})=\\\\=\sqrt[4]{8+2\sqrt{15}}*\sqrt{\sqrt{5}+\sqrt{3}}*( \sqrt{5}-\sqrt{3})=\\\\8+2\sqrt{15}=(5+3)+2\sqrt{5*3}=(\sqrt{5})^2+(\sqrt{3})^2+2\sqrt{5*3}=(\sqrt{5}+\sqrt{3})^2[/tex]

[tex]=\sqrt[4]{(\sqrt{5}+\sqrt{3})^2}*\sqrt{\sqrt{5}+\sqrt{3}}*(\sqrt{5}-\sqrt{3})=\\\\=\sqrt{\sqrt{5}+\sqrt{3}}* \sqrt{\sqrt{5}+\sqrt{3}}*(\sqrt{5}-\sqrt{3})=\\\\=\sqrt{(\sqrt{5}+\sqrt{3})^2}(\sqrt{5}-\sqrt{3}})=\\\\=(\sqrt{5}+\sqrt{3}}) (\sqrt{5}-\sqrt{3}})=(\sqrt{5})^2-(\sqrt{3})^2 =5-3=2[/tex]