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

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

\(\sqrt{300}=\sqrt{100}⋅\sqrt{3}=10\sqrt{3}\text{.}\)

\(-5\sqrt{125}=-5⋅\sqrt{25}⋅\sqrt{5}=-5⋅5⋅\sqrt{5}=-25\sqrt{5}\text{.}\)

\(2\sqrt{12}+4\sqrt{75}=2⋅\sqrt{4}⋅\sqrt{3}+4⋅\sqrt{25}⋅\sqrt{3}\text{.}\)

\(2⋅2⋅\sqrt{3}+4⋅5⋅\sqrt{3}=4\sqrt{3}+20\sqrt{3}=24\sqrt{3}\text{.}\)

\(\sqrt{1\frac{32}{49}}=\sqrt{\frac{81}{49}}={\sqrt{81} \over \sqrt{49}}=\frac{9}{7}=1\frac{2}{7}\text{.}\)

\({8 \over 7\sqrt{2}}={8 \over 7\sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={8\sqrt{2} \over 7⋅2}=\frac{4}{7}\sqrt{2}\text{.}\)

\(\sqrt{20\frac{3}{4}}=\sqrt{\frac{83}{4}}={\sqrt{83} \over \sqrt{4}}={\sqrt{83} \over 2}=\frac{1}{2}\sqrt{83}\text{.}\)

\(\sqrt{\frac{16}{63}}={\sqrt{16} \over \sqrt{63}}={4 \over \sqrt{63}}⋅{\sqrt{63} \over \sqrt{63}}={4\sqrt{63} \over 63}=\frac{4}{63}\sqrt{63}=\frac{4}{63}⋅3⋅\sqrt{7}=\frac{4}{21}\sqrt{7}\text{.}\)

\(\sqrt{37\frac{1}{2}}=\sqrt{\frac{75}{2}}={\sqrt{75} \over \sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={\sqrt{150} \over 2}=\frac{1}{2}\sqrt{150}=\frac{1}{2}⋅5⋅\sqrt{6}=2\frac{1}{2}\sqrt{6}\text{.}\)

\({21\sqrt{120} \over 3\sqrt{10}}={21 \over 3}⋅{\sqrt{120} \over \sqrt{10}}=7\sqrt{12}=7⋅\sqrt{4}⋅\sqrt{3}=7⋅2⋅\sqrt{3}=14\sqrt{3}\)

\(5\sqrt{10}⋅3\sqrt{2}=15\sqrt{20}=15⋅\sqrt{4}⋅\sqrt{5}=15⋅2⋅\sqrt{5}=30\sqrt{5}\)