Question

Заранее спасибо.........​

Answer 1

$\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5} } =\sqrt{\frac{6-2\sqrt{5} }{2}}+\sqrt{\frac{6+2\sqrt{5} }{2}}=\sqrt{\frac{(\sqrt{5})^{2}-2\sqrt{5}+1^{2}}{2} }+\sqrt{\frac{(\sqrt{5})^{2}+2\sqrt{5}+1^{2}}{2} }=\\\\=\sqrt{\frac{(\sqrt{5}-1)^{2}}{2}}+\sqrt{\frac{(\sqrt{5}+1)^{2}}{2}}=\frac{|\sqrt{5}-1| }{\sqrt{2}}+\frac{|\sqrt{5}+1| }{\sqrt{2}}=\frac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}=\\\\=\frac{2\sqrt{5}}{\sqrt{2}} =\boxed{\sqrt{10} }$