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

\(7\sqrt{50}=7⋅\sqrt{25}⋅\sqrt{2}=7⋅5⋅\sqrt{2}=35\sqrt{2}\text{.}\)

\(\sqrt{\frac{9}{25}}={\sqrt{9} \over \sqrt{25}}=\frac{3}{5}\text{.}\)

\(\sqrt{1\frac{3}{49}}=\sqrt{\frac{52}{49}}={\sqrt{52} \over \sqrt{49}}={\sqrt{52} \over 7}=\frac{1}{7}\sqrt{52}=\frac{1}{7}⋅2⋅\sqrt{13}=\frac{2}{7}\sqrt{13}\text{.}\)

\(\sqrt{75}+\sqrt{12}=\sqrt{25}⋅\sqrt{3}+\sqrt{4}⋅\sqrt{3}=5\sqrt{3}+2\sqrt{3}\text{.}\)

\(5\sqrt{3}+2\sqrt{3}=7\sqrt{3}\text{.}\)

\(7\sqrt{48}+6\sqrt{27}=7⋅\sqrt{16}⋅\sqrt{3}+6⋅\sqrt{9}⋅\sqrt{3}\text{.}\)

\(7⋅4⋅\sqrt{3}+6⋅3⋅\sqrt{3}=28\sqrt{3}+18\sqrt{3}=46\sqrt{3}\text{.}\)

\({8 \over 5\sqrt{2}}={8 \over 5\sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={8\sqrt{2} \over 5⋅2}=\frac{4}{5}\sqrt{2}\text{.}\)

\(\sqrt{2\frac{1}{12}}=\sqrt{\frac{25}{12}}={\sqrt{25} \over \sqrt{12}}={5 \over \sqrt{12}}⋅{\sqrt{12} \over \sqrt{12}}={5\sqrt{12} \over 12}=\frac{5}{12}\sqrt{12}=\frac{5}{12}⋅2⋅\sqrt{3}=\frac{5}{6}\sqrt{3}\text{.}\)

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