Question

Answer 1

\(1+2\sqrt{5}\)

Answer 2

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

Answer 3

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