\(\sqrt{20}=\sqrt{4}⋅\sqrt{5}=2\sqrt{5}\text{.}\)

\(-2\sqrt{8}=-2⋅\sqrt{4}⋅\sqrt{2}=-2⋅2⋅\sqrt{2}=-4\sqrt{2}\text{.}\)

\(\sqrt{\frac{25}{49}}={\sqrt{25} \over \sqrt{49}}=\frac{5}{7}\text{.}\)

\(\sqrt{6\frac{1}{9}}=\sqrt{\frac{55}{9}}={\sqrt{55} \over \sqrt{9}}={\sqrt{55} \over 3}=\frac{1}{3}\sqrt{55}\text{.}\)

\(\sqrt{80}+\sqrt{20}=\sqrt{16}⋅\sqrt{5}+\sqrt{4}⋅\sqrt{5}=4\sqrt{5}+2\sqrt{5}\text{.}\)

\(4\sqrt{5}+2\sqrt{5}=6\sqrt{5}\text{.}\)

\(4\sqrt{500}-7\sqrt{45}=4⋅\sqrt{100}⋅\sqrt{5}-7⋅\sqrt{9}⋅\sqrt{5}\text{.}\)

\(4⋅10⋅\sqrt{5}-7⋅3⋅\sqrt{5}=40\sqrt{5}-21\sqrt{5}=19\sqrt{5}\text{.}\)

\({2 \over 3\sqrt{5}}={2 \over 3\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={2\sqrt{5} \over 3⋅5}=\frac{2}{15}\sqrt{5}\text{.}\)

\(\sqrt{2\frac{2}{31}}=\sqrt{\frac{64}{31}}={\sqrt{64} \over \sqrt{31}}={8 \over \sqrt{31}}⋅{\sqrt{31} \over \sqrt{31}}={8\sqrt{31} \over 31}=\frac{8}{31}\sqrt{31}\text{.}\)

\(\sqrt{4\frac{2}{3}}=\sqrt{\frac{14}{3}}={\sqrt{14} \over \sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={\sqrt{42} \over 3}=\frac{1}{3}\sqrt{42}\text{.}\)

\({20\sqrt{56} \over 5\sqrt{2}}={20 \over 5}⋅{\sqrt{56} \over \sqrt{2}}=4\sqrt{28}=4⋅\sqrt{4}⋅\sqrt{7}=4⋅2⋅\sqrt{7}=8\sqrt{7}\)

\(3\sqrt{15}⋅4\sqrt{6}=12\sqrt{90}=12⋅\sqrt{9}⋅\sqrt{10}=12⋅3⋅\sqrt{10}=36\sqrt{10}\)