\(\sqrt{27}+\sqrt{48}=\sqrt{9}⋅\sqrt{3}+\sqrt{16}⋅\sqrt{3}=3\sqrt{3}+4\sqrt{3}\text{.}\)

\(3\sqrt{3}+4\sqrt{3}=7\sqrt{3}\text{.}\)

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

\(7\sqrt{48}=7⋅\sqrt{16}⋅\sqrt{3}=7⋅4⋅\sqrt{3}=28\sqrt{3}\text{.}\)

\(5\sqrt{20}+3\sqrt{45}=5⋅\sqrt{4}⋅\sqrt{5}+3⋅\sqrt{9}⋅\sqrt{5}\text{.}\)

\(5⋅2⋅\sqrt{5}+3⋅3⋅\sqrt{5}=10\sqrt{5}+9\sqrt{5}=19\sqrt{5}\text{.}\)

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

\({3 \over 8\sqrt{5}}={3 \over 8\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={3\sqrt{5} \over 8⋅5}=\frac{3}{40}\sqrt{5}\text{.}\)

\(\sqrt{\frac{28}{81}}={\sqrt{28} \over \sqrt{81}}={\sqrt{28} \over 9}=\frac{1}{9}\sqrt{28}=\frac{1}{9}⋅2⋅\sqrt{7}=\frac{2}{9}\sqrt{7}\text{.}\)

\(\sqrt{1\frac{1}{35}}=\sqrt{\frac{36}{35}}={\sqrt{36} \over \sqrt{35}}={6 \over \sqrt{35}}⋅{\sqrt{35} \over \sqrt{35}}={6\sqrt{35} \over 35}=\frac{6}{35}\sqrt{35}\text{.}\)

\(\sqrt{1\frac{3}{7}}=\sqrt{\frac{10}{7}}={\sqrt{10} \over \sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={\sqrt{70} \over 7}=\frac{1}{7}\sqrt{70}\text{.}\)

\({48\sqrt{240} \over 6\sqrt{10}}={48 \over 6}⋅{\sqrt{240} \over \sqrt{10}}=8\sqrt{24}=8⋅\sqrt{4}⋅\sqrt{6}=8⋅2⋅\sqrt{6}=16\sqrt{6}\)

\(3\sqrt{14}⋅4\sqrt{7}=12\sqrt{98}=12⋅\sqrt{49}⋅\sqrt{2}=12⋅7⋅\sqrt{2}=84\sqrt{2}\)