\(\sqrt{28}=\sqrt{4}⋅\sqrt{7}=2\sqrt{7}\text{.}\)

\(5\sqrt{112}=5⋅\sqrt{16}⋅\sqrt{7}=5⋅4⋅\sqrt{7}=20\sqrt{7}\text{.}\)

\(\sqrt{1\frac{24}{25}}=\sqrt{\frac{49}{25}}={\sqrt{49} \over \sqrt{25}}=\frac{7}{5}=1\frac{2}{5}\text{.}\)

\(\sqrt{2\frac{4}{25}}=\sqrt{\frac{54}{25}}={\sqrt{54} \over \sqrt{25}}={\sqrt{54} \over 5}=\frac{1}{5}\sqrt{54}=\frac{1}{5}⋅3⋅\sqrt{6}=\frac{3}{5}\sqrt{6}\text{.}\)

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

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

\(3\sqrt{50}-5\sqrt{32}=3⋅\sqrt{25}⋅\sqrt{2}-5⋅\sqrt{16}⋅\sqrt{2}\text{.}\)

\(3⋅5⋅\sqrt{2}-5⋅4⋅\sqrt{2}=15\sqrt{2}-20\sqrt{2}=-5\sqrt{2}\text{.}\)

\({9 \over 5\sqrt{3}}={9 \over 5\sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={9\sqrt{3} \over 5⋅3}=\frac{3}{5}\sqrt{3}\text{.}\)

\(\sqrt{\frac{1}{50}}={\sqrt{1} \over \sqrt{50}}={1 \over \sqrt{50}}⋅{\sqrt{50} \over \sqrt{50}}={\sqrt{50} \over 50}=\frac{1}{50}\sqrt{50}=\frac{1}{50}⋅5⋅\sqrt{2}=\frac{1}{10}\sqrt{2}\text{.}\)

\(\sqrt{\frac{2}{13}}={\sqrt{2} \over \sqrt{13}}⋅{\sqrt{13} \over \sqrt{13}}={\sqrt{26} \over 13}=\frac{1}{13}\sqrt{26}\text{.}\)

\({40\sqrt{100} \over 5\sqrt{5}}={40 \over 5}⋅{\sqrt{100} \over \sqrt{5}}=8\sqrt{20}=8⋅\sqrt{4}⋅\sqrt{5}=8⋅2⋅\sqrt{5}=16\sqrt{5}\)

\(3\sqrt{6}⋅2\sqrt{3}=6\sqrt{18}=6⋅\sqrt{9}⋅\sqrt{2}=6⋅3⋅\sqrt{2}=18\sqrt{2}\)