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

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

\(\sqrt{1\frac{15}{49}}=\sqrt{\frac{64}{49}}={\sqrt{64} \over \sqrt{49}}=\frac{8}{7}=1\frac{1}{7}\text{.}\)

\(\sqrt{3\frac{5}{9}}=\sqrt{\frac{32}{9}}={\sqrt{32} \over \sqrt{9}}={\sqrt{32} \over 3}=\frac{1}{3}\sqrt{32}=\frac{1}{3}⋅4⋅\sqrt{2}=1\frac{1}{3}\sqrt{2}\text{.}\)

\(\sqrt{75}+\sqrt{27}=\sqrt{25}⋅\sqrt{3}+\sqrt{9}⋅\sqrt{3}=5\sqrt{3}+3\sqrt{3}\text{.}\)

\(5\sqrt{3}+3\sqrt{3}=8\sqrt{3}\text{.}\)

\(7\sqrt{32}-5\sqrt{50}=7⋅\sqrt{16}⋅\sqrt{2}-5⋅\sqrt{25}⋅\sqrt{2}\text{.}\)

\(7⋅4⋅\sqrt{2}-5⋅5⋅\sqrt{2}=28\sqrt{2}-25\sqrt{2}=3\sqrt{2}\text{.}\)

\({8 \over 3\sqrt{2}}={8 \over 3\sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={8\sqrt{2} \over 3⋅2}=1\frac{1}{3}\sqrt{2}\text{.}\)

\(\sqrt{6\frac{3}{13}}=\sqrt{\frac{81}{13}}={\sqrt{81} \over \sqrt{13}}={9 \over \sqrt{13}}⋅{\sqrt{13} \over \sqrt{13}}={9\sqrt{13} \over 13}=\frac{9}{13}\sqrt{13}\text{.}\)

\(\sqrt{\frac{7}{50}}={\sqrt{7} \over \sqrt{50}}⋅{\sqrt{50} \over \sqrt{50}}={\sqrt{350} \over 50}=\frac{1}{50}\sqrt{350}=\frac{1}{50}⋅5⋅\sqrt{14}=\frac{1}{10}\sqrt{14}\text{.}\)

\({9\sqrt{240} \over \sqrt{10}}=9⋅{\sqrt{240} \over \sqrt{10}}=9\sqrt{24}=9⋅\sqrt{4}⋅\sqrt{6}=9⋅2⋅\sqrt{6}=18\sqrt{6}\)

\(2\sqrt{2}⋅4\sqrt{6}=8\sqrt{12}=8⋅\sqrt{4}⋅\sqrt{3}=8⋅2⋅\sqrt{3}=16\sqrt{3}\)