Question

Answer 1

\(=\left(\sqrt[5]{\dfrac{1}{5}}+\dfrac{1}{20}\cdot2\sqrt{5}-\dfrac{5}{4}\sqrt{4\left(\dfrac{1}{5}+\dfrac{\sqrt{5}}{4}\right)}\right):2\sqrt{5}\)
\(=\left(\sqrt[5]{\dfrac{1}{5}}+\dfrac{1}{10}\sqrt{5}-\dfrac{5}{4}\cdot2\cdot\sqrt{\dfrac{4+5\sqrt{5}}{20}}\right):2\sqrt{5}\)

\(=\left(\sqrt[5]{\dfrac{1}{5}}+\dfrac{1}{10}\sqrt{5}-\dfrac{\sqrt{5}\left(\sqrt{4+5\sqrt{5}}\right)}{4}\right):2\sqrt{5}\)

\(=\sqrt[5]{\dfrac{1}{5}}:2\sqrt{5}+\dfrac{1}{20}-\dfrac{\sqrt{4+5\sqrt{5}}}{8}\)