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

\(-5\sqrt{700}=-5⋅\sqrt{100}⋅\sqrt{7}=-5⋅10⋅\sqrt{7}=-50\sqrt{7}\text{.}\)

\(\sqrt{7\frac{1}{9}}=\sqrt{\frac{64}{9}}={\sqrt{64} \over \sqrt{9}}=\frac{8}{3}=2\frac{2}{3}\text{.}\)

\(\sqrt{\frac{32}{49}}={\sqrt{32} \over \sqrt{49}}={\sqrt{32} \over 7}=\frac{1}{7}\sqrt{32}=\frac{1}{7}⋅4⋅\sqrt{2}=\frac{4}{7}\sqrt{2}\text{.}\)

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

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

\(6\sqrt{12}+2\sqrt{75}=6⋅\sqrt{4}⋅\sqrt{3}+2⋅\sqrt{25}⋅\sqrt{3}\text{.}\)

\(6⋅2⋅\sqrt{3}+2⋅5⋅\sqrt{3}=12\sqrt{3}+10\sqrt{3}=22\sqrt{3}\text{.}\)

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

\(\sqrt{\frac{4}{57}}={\sqrt{4} \over \sqrt{57}}={2 \over \sqrt{57}}⋅{\sqrt{57} \over \sqrt{57}}={2\sqrt{57} \over 57}=\frac{2}{57}\sqrt{57}\text{.}\)

\(\sqrt{13\frac{1}{2}}=\sqrt{\frac{27}{2}}={\sqrt{27} \over \sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={\sqrt{54} \over 2}=\frac{1}{2}\sqrt{54}=\frac{1}{2}⋅3⋅\sqrt{6}=1\frac{1}{2}\sqrt{6}\text{.}\)

\({3\sqrt{240} \over \sqrt{6}}=3⋅{\sqrt{240} \over \sqrt{6}}=3\sqrt{40}=3⋅\sqrt{4}⋅\sqrt{10}=3⋅2⋅\sqrt{10}=6\sqrt{10}\)

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