\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
\(=\dfrac{\sqrt{3-\sqrt{5}}\cdot\sqrt{2}}{\sqrt{2}}+\dfrac{\sqrt{3+\sqrt{5}}\cdot\sqrt{2}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{5-2\sqrt{5}+1}+\sqrt{5+2\sqrt{5}+1}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}\)
\(=\dfrac{\left|\sqrt{5}-1\right|+\left|\sqrt{5}+1\right|}{\sqrt{2}}\)
\(=\dfrac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}\) ( vì \(\sqrt{5}-1>0\) , \(\sqrt{5}+1>0\) )
\(=\dfrac{2\sqrt{5}}{\sqrt{2}}\\ =\sqrt{2}\cdot\sqrt{5}\\ =\sqrt{10}\)
=1/căn 2(căn 5-1+căn 5+1)
=1/căn 2*2căn 5
=căn 10
