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

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

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

\(-4\sqrt{175}=-4⋅\sqrt{25}⋅\sqrt{7}=-4⋅5⋅\sqrt{7}=-20\sqrt{7}\text{.}\)

\(3\sqrt{125}-5\sqrt{45}=3⋅\sqrt{25}⋅\sqrt{5}-5⋅\sqrt{9}⋅\sqrt{5}\text{.}\)

\(3⋅5⋅\sqrt{5}-5⋅3⋅\sqrt{5}=15\sqrt{5}-15\sqrt{5}=0\sqrt{5}\text{.}\)

\(\sqrt{\frac{1}{81}}={\sqrt{1} \over \sqrt{81}}=\frac{1}{9}\text{.}\)

\({7 \over 8\sqrt{5}}={7 \over 8\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={7\sqrt{5} \over 8⋅5}=\frac{7}{40}\sqrt{5}\text{.}\)

\(\sqrt{1\frac{13}{16}}=\sqrt{\frac{29}{16}}={\sqrt{29} \over \sqrt{16}}={\sqrt{29} \over 4}=\frac{1}{4}\sqrt{29}\text{.}\)

\(\sqrt{\frac{1}{75}}={\sqrt{1} \over \sqrt{75}}={1 \over \sqrt{75}}⋅{\sqrt{75} \over \sqrt{75}}={\sqrt{75} \over 75}=\frac{1}{75}\sqrt{75}=\frac{1}{75}⋅5⋅\sqrt{3}=\frac{1}{15}\sqrt{3}\text{.}\)

\(\sqrt{2\frac{1}{5}}=\sqrt{\frac{11}{5}}={\sqrt{11} \over \sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={\sqrt{55} \over 5}=\frac{1}{5}\sqrt{55}\text{.}\)

\({12\sqrt{96} \over 3\sqrt{8}}={12 \over 3}⋅{\sqrt{96} \over \sqrt{8}}=4\sqrt{12}=4⋅\sqrt{4}⋅\sqrt{3}=4⋅2⋅\sqrt{3}=8\sqrt{3}\)

\(4\sqrt{15}⋅5\sqrt{3}=20\sqrt{45}=20⋅\sqrt{9}⋅\sqrt{5}=20⋅3⋅\sqrt{5}=60\sqrt{5}\)