\(\sqrt{8}+\sqrt{18}=\sqrt{4}⋅\sqrt{2}+\sqrt{9}⋅\sqrt{2}=2\sqrt{2}+3\sqrt{2}\text{.}\)

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

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

\(2\sqrt{12}=2⋅\sqrt{4}⋅\sqrt{3}=2⋅2⋅\sqrt{3}=4\sqrt{3}\text{.}\)

\(6\sqrt{125}+3\sqrt{45}=6⋅\sqrt{25}⋅\sqrt{5}+3⋅\sqrt{9}⋅\sqrt{5}\text{.}\)

\(6⋅5⋅\sqrt{5}+3⋅3⋅\sqrt{5}=30\sqrt{5}+9\sqrt{5}=39\sqrt{5}\text{.}\)

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

\({4 \over 3\sqrt{2}}={4 \over 3\sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={4\sqrt{2} \over 3⋅2}=\frac{2}{3}\sqrt{2}\text{.}\)

\(\sqrt{20\frac{3}{4}}=\sqrt{\frac{83}{4}}={\sqrt{83} \over \sqrt{4}}={\sqrt{83} \over 2}=\frac{1}{2}\sqrt{83}\text{.}\)

\(\sqrt{\frac{16}{27}}={\sqrt{16} \over \sqrt{27}}={4 \over \sqrt{27}}⋅{\sqrt{27} \over \sqrt{27}}={4\sqrt{27} \over 27}=\frac{4}{27}\sqrt{27}=\frac{4}{27}⋅3⋅\sqrt{3}=\frac{4}{9}\sqrt{3}\text{.}\)

\(\sqrt{\frac{5}{6}}={\sqrt{5} \over \sqrt{6}}⋅{\sqrt{6} \over \sqrt{6}}={\sqrt{30} \over 6}=\frac{1}{6}\sqrt{30}\text{.}\)

\({20\sqrt{36} \over 4\sqrt{3}}={20 \over 4}⋅{\sqrt{36} \over \sqrt{3}}=5\sqrt{12}=5⋅\sqrt{4}⋅\sqrt{3}=5⋅2⋅\sqrt{3}=10\sqrt{3}\)

\(5\sqrt{6}⋅2\sqrt{15}=10\sqrt{90}=10⋅\sqrt{9}⋅\sqrt{10}=10⋅3⋅\sqrt{10}=30\sqrt{10}\)