\(\sqrt{20}+\sqrt{125}=\sqrt{4}⋅\sqrt{5}+\sqrt{25}⋅\sqrt{5}=2\sqrt{5}+5\sqrt{5}\text{.}\)

\(2\sqrt{5}+5\sqrt{5}=7\sqrt{5}\text{.}\)

\(\sqrt{112}=\sqrt{16}⋅\sqrt{7}=4\sqrt{7}\text{.}\)

\(7\sqrt{18}=7⋅\sqrt{9}⋅\sqrt{2}=7⋅3⋅\sqrt{2}=21\sqrt{2}\text{.}\)

\(6\sqrt{300}+5\sqrt{75}=6⋅\sqrt{100}⋅\sqrt{3}+5⋅\sqrt{25}⋅\sqrt{3}\text{.}\)

\(6⋅10⋅\sqrt{3}+5⋅5⋅\sqrt{3}=60\sqrt{3}+25\sqrt{3}=85\sqrt{3}\text{.}\)

\(\sqrt{11\frac{1}{9}}=\sqrt{\frac{100}{9}}={\sqrt{100} \over \sqrt{9}}=\frac{10}{3}=3\frac{1}{3}\text{.}\)

\({5 \over 2\sqrt{2}}={5 \over 2\sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={5\sqrt{2} \over 2⋅2}=1\frac{1}{4}\sqrt{2}\text{.}\)

\(\sqrt{\frac{73}{100}}={\sqrt{73} \over \sqrt{100}}={\sqrt{73} \over 10}=\frac{1}{10}\sqrt{73}\text{.}\)

\(\sqrt{1\frac{3}{61}}=\sqrt{\frac{64}{61}}={\sqrt{64} \over \sqrt{61}}={8 \over \sqrt{61}}⋅{\sqrt{61} \over \sqrt{61}}={8\sqrt{61} \over 61}=\frac{8}{61}\sqrt{61}\text{.}\)

\(\sqrt{9\frac{3}{8}}=\sqrt{\frac{75}{8}}={\sqrt{75} \over \sqrt{8}}⋅{\sqrt{8} \over \sqrt{8}}={\sqrt{600} \over 8}=\frac{1}{8}\sqrt{600}=\frac{1}{8}⋅10⋅\sqrt{6}=1\frac{1}{4}\sqrt{6}\text{.}\)

\({18\sqrt{56} \over 6\sqrt{7}}={18 \over 6}⋅{\sqrt{56} \over \sqrt{7}}=3\sqrt{8}=3⋅\sqrt{4}⋅\sqrt{2}=3⋅2⋅\sqrt{2}=6\sqrt{2}\)

\(5\sqrt{5}⋅4\sqrt{15}=20\sqrt{75}=20⋅\sqrt{25}⋅\sqrt{3}=20⋅5⋅\sqrt{3}=100\sqrt{3}\)