\(\sqrt{48}+\sqrt{300}=\sqrt{16}⋅\sqrt{3}+\sqrt{100}⋅\sqrt{3}=4\sqrt{3}+10\sqrt{3}\text{.}\)

\(4\sqrt{3}+10\sqrt{3}=14\sqrt{3}\text{.}\)

\(\sqrt{32}=\sqrt{16}⋅\sqrt{2}=4\sqrt{2}\text{.}\)

\(2\sqrt{63}=2⋅\sqrt{9}⋅\sqrt{7}=2⋅3⋅\sqrt{7}=6\sqrt{7}\text{.}\)

\(6\sqrt{8}+3\sqrt{200}=6⋅\sqrt{4}⋅\sqrt{2}+3⋅\sqrt{100}⋅\sqrt{2}\text{.}\)

\(6⋅2⋅\sqrt{2}+3⋅10⋅\sqrt{2}=12\sqrt{2}+30\sqrt{2}=42\sqrt{2}\text{.}\)

\(\sqrt{\frac{64}{81}}={\sqrt{64} \over \sqrt{81}}=\frac{8}{9}\text{.}\)

\({4 \over 5\sqrt{5}}={4 \over 5\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={4\sqrt{5} \over 5⋅5}=\frac{4}{25}\sqrt{5}\text{.}\)

\(\sqrt{\frac{5}{36}}={\sqrt{5} \over \sqrt{36}}={\sqrt{5} \over 6}=\frac{1}{6}\sqrt{5}\text{.}\)

\(\sqrt{\frac{49}{90}}={\sqrt{49} \over \sqrt{90}}={7 \over \sqrt{90}}⋅{\sqrt{90} \over \sqrt{90}}={7\sqrt{90} \over 90}=\frac{7}{90}\sqrt{90}=\frac{7}{90}⋅3⋅\sqrt{10}=\frac{7}{30}\sqrt{10}\text{.}\)

\(\sqrt{6\frac{1}{3}}=\sqrt{\frac{19}{3}}={\sqrt{19} \over \sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={\sqrt{57} \over 3}=\frac{1}{3}\sqrt{57}\text{.}\)

\({2\sqrt{140} \over \sqrt{7}}=2⋅{\sqrt{140} \over \sqrt{7}}=2\sqrt{20}=2⋅\sqrt{4}⋅\sqrt{5}=2⋅2⋅\sqrt{5}=4\sqrt{5}\)

\(5\sqrt{7}⋅3\sqrt{14}=15\sqrt{98}=15⋅\sqrt{49}⋅\sqrt{2}=15⋅7⋅\sqrt{2}=105\sqrt{2}\)