\(\dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{2}}=\dfrac{\sqrt{6-2\sqrt{5}}}{2}=\dfrac{\sqrt{\left(\sqrt{5}-1\right)^2}}{2}=\dfrac{\sqrt{5}-1}{2}\)
\(\sqrt{3-\sqrt{5}}:\sqrt{2}\) =\(\dfrac{\sqrt{2}.\sqrt{3-\sqrt{5}}}{\sqrt{2}.\sqrt{2}}\)=\(\dfrac{\sqrt{5}-1}{2}\)