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

\(-5\sqrt{200}=-5⋅\sqrt{100}⋅\sqrt{2}=-5⋅10⋅\sqrt{2}=-50\sqrt{2}\text{.}\)

\(\sqrt{\frac{9}{64}}={\sqrt{9} \over \sqrt{64}}=\frac{3}{8}\text{.}\)

\(\sqrt{16\frac{1}{4}}=\sqrt{\frac{65}{4}}={\sqrt{65} \over \sqrt{4}}={\sqrt{65} \over 2}=\frac{1}{2}\sqrt{65}\text{.}\)

\(\sqrt{18}+\sqrt{32}=\sqrt{9}⋅\sqrt{2}+\sqrt{16}⋅\sqrt{2}=3\sqrt{2}+4\sqrt{2}\text{.}\)

\(3\sqrt{2}+4\sqrt{2}=7\sqrt{2}\text{.}\)

\(7\sqrt{27}+6\sqrt{300}=7⋅\sqrt{9}⋅\sqrt{3}+6⋅\sqrt{100}⋅\sqrt{3}\text{.}\)

\(7⋅3⋅\sqrt{3}+6⋅10⋅\sqrt{3}=21\sqrt{3}+60\sqrt{3}=81\sqrt{3}\text{.}\)

\({7 \over 2\sqrt{2}}={7 \over 2\sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={7\sqrt{2} \over 2⋅2}=1\frac{3}{4}\sqrt{2}\text{.}\)

\(\sqrt{1\frac{1}{80}}=\sqrt{\frac{81}{80}}={\sqrt{81} \over \sqrt{80}}={9 \over \sqrt{80}}⋅{\sqrt{80} \over \sqrt{80}}={9\sqrt{80} \over 80}=\frac{9}{80}\sqrt{80}=\frac{9}{80}⋅4⋅\sqrt{5}=\frac{9}{20}\sqrt{5}\text{.}\)

\(\sqrt{\frac{2}{43}}={\sqrt{2} \over \sqrt{43}}⋅{\sqrt{43} \over \sqrt{43}}={\sqrt{86} \over 43}=\frac{1}{43}\sqrt{86}\text{.}\)