\(\sqrt{48}+\sqrt{12}=\sqrt{16}⋅\sqrt{3}+\sqrt{4}⋅\sqrt{3}=4\sqrt{3}+2\sqrt{3}\text{.}\)

\(4\sqrt{3}+2\sqrt{3}=6\sqrt{3}\text{.}\)

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

\(-3\sqrt{28}=-3⋅\sqrt{4}⋅\sqrt{7}=-3⋅2⋅\sqrt{7}=-6\sqrt{7}\text{.}\)

\(2\sqrt{500}-5\sqrt{20}=2⋅\sqrt{100}⋅\sqrt{5}-5⋅\sqrt{4}⋅\sqrt{5}\text{.}\)

\(2⋅10⋅\sqrt{5}-5⋅2⋅\sqrt{5}=20\sqrt{5}-10\sqrt{5}=10\sqrt{5}\text{.}\)

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

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

\(\sqrt{6\frac{3}{4}}=\sqrt{\frac{27}{4}}={\sqrt{27} \over \sqrt{4}}={\sqrt{27} \over 2}=\frac{1}{2}\sqrt{27}=\frac{1}{2}⋅3⋅\sqrt{3}=1\frac{1}{2}\sqrt{3}\text{.}\)

\(\sqrt{1\frac{37}{44}}=\sqrt{\frac{81}{44}}={\sqrt{81} \over \sqrt{44}}={9 \over \sqrt{44}}⋅{\sqrt{44} \over \sqrt{44}}={9\sqrt{44} \over 44}=\frac{9}{44}\sqrt{44}=\frac{9}{44}⋅2⋅\sqrt{11}=\frac{9}{22}\sqrt{11}\text{.}\)

\(\sqrt{\frac{5}{14}}={\sqrt{5} \over \sqrt{14}}⋅{\sqrt{14} \over \sqrt{14}}={\sqrt{70} \over 14}=\frac{1}{14}\sqrt{70}\text{.}\)

\({54\sqrt{120} \over 6\sqrt{3}}={54 \over 6}⋅{\sqrt{120} \over \sqrt{3}}=9\sqrt{40}=9⋅\sqrt{4}⋅\sqrt{10}=9⋅2⋅\sqrt{10}=18\sqrt{10}\)

\(3\sqrt{6}⋅5\sqrt{2}=15\sqrt{12}=15⋅\sqrt{4}⋅\sqrt{3}=15⋅2⋅\sqrt{3}=30\sqrt{3}\)