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

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

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

\(-4\sqrt{20}=-4⋅\sqrt{4}⋅\sqrt{5}=-4⋅2⋅\sqrt{5}=-8\sqrt{5}\text{.}\)

\(5\sqrt{18}+3\sqrt{32}=5⋅\sqrt{9}⋅\sqrt{2}+3⋅\sqrt{16}⋅\sqrt{2}\text{.}\)

\(5⋅3⋅\sqrt{2}+3⋅4⋅\sqrt{2}=15\sqrt{2}+12\sqrt{2}=27\sqrt{2}\text{.}\)

\(\sqrt{20\frac{1}{4}}=\sqrt{\frac{81}{4}}={\sqrt{81} \over \sqrt{4}}=\frac{9}{2}=4\frac{1}{2}\text{.}\)

\({9 \over 4\sqrt{5}}={9 \over 4\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={9\sqrt{5} \over 4⋅5}=\frac{9}{20}\sqrt{5}\text{.}\)

\(\sqrt{\frac{21}{64}}={\sqrt{21} \over \sqrt{64}}={\sqrt{21} \over 8}=\frac{1}{8}\sqrt{21}\text{.}\)

\(\sqrt{1\frac{1}{48}}=\sqrt{\frac{49}{48}}={\sqrt{49} \over \sqrt{48}}={7 \over \sqrt{48}}⋅{\sqrt{48} \over \sqrt{48}}={7\sqrt{48} \over 48}=\frac{7}{48}\sqrt{48}=\frac{7}{48}⋅4⋅\sqrt{3}=\frac{7}{12}\sqrt{3}\text{.}\)

\(\sqrt{\frac{2}{23}}={\sqrt{2} \over \sqrt{23}}⋅{\sqrt{23} \over \sqrt{23}}={\sqrt{46} \over 23}=\frac{1}{23}\sqrt{46}\text{.}\)

\({30\sqrt{192} \over 6\sqrt{8}}={30 \over 6}⋅{\sqrt{192} \over \sqrt{8}}=5\sqrt{24}=5⋅\sqrt{4}⋅\sqrt{6}=5⋅2⋅\sqrt{6}=10\sqrt{6}\)

\(2\sqrt{10}⋅5\sqrt{5}=10\sqrt{50}=10⋅\sqrt{25}⋅\sqrt{2}=10⋅5⋅\sqrt{2}=50\sqrt{2}\)