\(5\sqrt{\dfrac{1}{2}}+\dfrac{1}{2}\sqrt{20}+\sqrt{5}\)
\(=\dfrac{5\sqrt{2}}{2}+\sqrt{5}+\sqrt{5}=\dfrac{5\sqrt{2}}{2}+2\sqrt{5}\)
\(=\dfrac{5\sqrt{2}}{2}+\dfrac{4\sqrt{5}}{2}=\dfrac{5\sqrt{2}+4\sqrt{5}}{2}\)
\(5\sqrt{\dfrac{1}{2}}+\dfrac{1}{2}\sqrt{20}+\sqrt{5}=\dfrac{5}{\sqrt{2}}+\dfrac{\sqrt{20}}{2}+\sqrt{5}=\dfrac{5\sqrt{2}+\sqrt{20}}{2}+\sqrt{5}=\dfrac{\sqrt{50}+\sqrt{20}}{\sqrt{4}}+\sqrt{5}=\dfrac{\sqrt{10}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{4}}+\sqrt{5}=\dfrac{\sqrt{5}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}+\sqrt{5}=\dfrac{5+\sqrt{10}+\sqrt{10}}{\sqrt{2}}=\dfrac{5+2\sqrt{10}}{\sqrt{2}}\)
