\(\sqrt{80}+\sqrt{500}=\sqrt{16}⋅\sqrt{5}+\sqrt{100}⋅\sqrt{5}=4\sqrt{5}+10\sqrt{5}\text{.}\)

\(4\sqrt{5}+10\sqrt{5}=14\sqrt{5}\text{.}\)

\(\sqrt{18}=\sqrt{9}⋅\sqrt{2}=3\sqrt{2}\text{.}\)

\(5\sqrt{300}=5⋅\sqrt{100}⋅\sqrt{3}=5⋅10⋅\sqrt{3}=50\sqrt{3}\text{.}\)

\(2\sqrt{12}-4\sqrt{300}=2⋅\sqrt{4}⋅\sqrt{3}-4⋅\sqrt{100}⋅\sqrt{3}\text{.}\)

\(2⋅2⋅\sqrt{3}-4⋅10⋅\sqrt{3}=4\sqrt{3}-40\sqrt{3}=-36\sqrt{3}\text{.}\)

\(\sqrt{1\frac{11}{25}}=\sqrt{\frac{36}{25}}={\sqrt{36} \over \sqrt{25}}=\frac{6}{5}=1\frac{1}{5}\text{.}\)

\({3 \over 4\sqrt{7}}={3 \over 4\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={3\sqrt{7} \over 4⋅7}=\frac{3}{28}\sqrt{7}\text{.}\)

\(\sqrt{\frac{19}{100}}={\sqrt{19} \over \sqrt{100}}={\sqrt{19} \over 10}=\frac{1}{10}\sqrt{19}\text{.}\)

\(\sqrt{2\frac{17}{32}}=\sqrt{\frac{81}{32}}={\sqrt{81} \over \sqrt{32}}={9 \over \sqrt{32}}⋅{\sqrt{32} \over \sqrt{32}}={9\sqrt{32} \over 32}=\frac{9}{32}\sqrt{32}=\frac{9}{32}⋅4⋅\sqrt{2}=1\frac{1}{8}\sqrt{2}\text{.}\)

\(\sqrt{\frac{3}{28}}={\sqrt{3} \over \sqrt{28}}⋅{\sqrt{28} \over \sqrt{28}}={\sqrt{84} \over 28}=\frac{1}{28}\sqrt{84}=\frac{1}{28}⋅2⋅\sqrt{21}=\frac{1}{14}\sqrt{21}\text{.}\)

\({36\sqrt{48} \over 4\sqrt{6}}={36 \over 4}⋅{\sqrt{48} \over \sqrt{6}}=9\sqrt{8}=9⋅\sqrt{4}⋅\sqrt{2}=9⋅2⋅\sqrt{2}=18\sqrt{2}\)

\(4\sqrt{6}⋅5\sqrt{3}=20\sqrt{18}=20⋅\sqrt{9}⋅\sqrt{2}=20⋅3⋅\sqrt{2}=60\sqrt{2}\)