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

\(4\sqrt{700}=4⋅\sqrt{100}⋅\sqrt{7}=4⋅10⋅\sqrt{7}=40\sqrt{7}\text{.}\)

\(\sqrt{11\frac{1}{9}}=\sqrt{\frac{100}{9}}={\sqrt{100} \over \sqrt{9}}=\frac{10}{3}=3\frac{1}{3}\text{.}\)

\(\sqrt{\frac{45}{64}}={\sqrt{45} \over \sqrt{64}}={\sqrt{45} \over 8}=\frac{1}{8}\sqrt{45}=\frac{1}{8}⋅3⋅\sqrt{5}=\frac{3}{8}\sqrt{5}\text{.}\)

\(\sqrt{125}+\sqrt{80}=\sqrt{25}⋅\sqrt{5}+\sqrt{16}⋅\sqrt{5}=5\sqrt{5}+4\sqrt{5}\text{.}\)

\(5\sqrt{5}+4\sqrt{5}=9\sqrt{5}\text{.}\)

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

\(2⋅4⋅\sqrt{2}+5⋅5⋅\sqrt{2}=8\sqrt{2}+25\sqrt{2}=33\sqrt{2}\text{.}\)

\({2 \over 3\sqrt{7}}={2 \over 3\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={2\sqrt{7} \over 3⋅7}=\frac{2}{21}\sqrt{7}\text{.}\)

\(\sqrt{3\frac{1}{8}}=\sqrt{\frac{25}{8}}={\sqrt{25} \over \sqrt{8}}={5 \over \sqrt{8}}⋅{\sqrt{8} \over \sqrt{8}}={5\sqrt{8} \over 8}=\frac{5}{8}\sqrt{8}=\frac{5}{8}⋅2⋅\sqrt{2}=1\frac{1}{4}\sqrt{2}\text{.}\)

\(\sqrt{\frac{3}{20}}={\sqrt{3} \over \sqrt{20}}⋅{\sqrt{20} \over \sqrt{20}}={\sqrt{60} \over 20}=\frac{1}{20}\sqrt{60}=\frac{1}{20}⋅2⋅\sqrt{15}=\frac{1}{10}\sqrt{15}\text{.}\)

\({32\sqrt{144} \over 4\sqrt{6}}={32 \over 4}⋅{\sqrt{144} \over \sqrt{6}}=8\sqrt{24}=8⋅\sqrt{4}⋅\sqrt{6}=8⋅2⋅\sqrt{6}=16\sqrt{6}\)

\(4\sqrt{7}⋅5\sqrt{14}=20\sqrt{98}=20⋅\sqrt{49}⋅\sqrt{2}=20⋅7⋅\sqrt{2}=140\sqrt{2}\)