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

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

\(\sqrt{300}=\sqrt{100}⋅\sqrt{3}=10\sqrt{3}\text{.}\)

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

\(7\sqrt{18}-4\sqrt{8}=7⋅\sqrt{9}⋅\sqrt{2}-4⋅\sqrt{4}⋅\sqrt{2}\text{.}\)

\(7⋅3⋅\sqrt{2}-4⋅2⋅\sqrt{2}=21\sqrt{2}-8\sqrt{2}=13\sqrt{2}\text{.}\)

\(\sqrt{5\frac{4}{9}}=\sqrt{\frac{49}{9}}={\sqrt{49} \over \sqrt{9}}=\frac{7}{3}=2\frac{1}{3}\text{.}\)

\({3 \over 7\sqrt{2}}={3 \over 7\sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={3\sqrt{2} \over 7⋅2}=\frac{3}{14}\sqrt{2}\text{.}\)

\(\sqrt{1\frac{29}{36}}=\sqrt{\frac{65}{36}}={\sqrt{65} \over \sqrt{36}}={\sqrt{65} \over 6}=\frac{1}{6}\sqrt{65}\text{.}\)

\(\sqrt{\frac{1}{59}}={\sqrt{1} \over \sqrt{59}}={1 \over \sqrt{59}}⋅{\sqrt{59} \over \sqrt{59}}={\sqrt{59} \over 59}=\frac{1}{59}\sqrt{59}\text{.}\)

\(\sqrt{\frac{3}{32}}={\sqrt{3} \over \sqrt{32}}⋅{\sqrt{32} \over \sqrt{32}}={\sqrt{96} \over 32}=\frac{1}{32}\sqrt{96}=\frac{1}{32}⋅4⋅\sqrt{6}=\frac{1}{8}\sqrt{6}\text{.}\)

\({48\sqrt{120} \over 6\sqrt{3}}={48 \over 6}⋅{\sqrt{120} \over \sqrt{3}}=8\sqrt{40}=8⋅\sqrt{4}⋅\sqrt{10}=8⋅2⋅\sqrt{10}=16\sqrt{10}\)

\(4\sqrt{2}⋅2\sqrt{14}=8\sqrt{28}=8⋅\sqrt{4}⋅\sqrt{7}=8⋅2⋅\sqrt{7}=16\sqrt{7}\)