\(\sqrt{200}+\sqrt{18}=\sqrt{100}⋅\sqrt{2}+\sqrt{9}⋅\sqrt{2}=10\sqrt{2}+3\sqrt{2}\text{.}\)

\(10\sqrt{2}+3\sqrt{2}=13\sqrt{2}\text{.}\)

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

\(7\sqrt{125}=7⋅\sqrt{25}⋅\sqrt{5}=7⋅5⋅\sqrt{5}=35\sqrt{5}\text{.}\)

\(2\sqrt{75}-7\sqrt{12}=2⋅\sqrt{25}⋅\sqrt{3}-7⋅\sqrt{4}⋅\sqrt{3}\text{.}\)

\(2⋅5⋅\sqrt{3}-7⋅2⋅\sqrt{3}=10\sqrt{3}-14\sqrt{3}=-4\sqrt{3}\text{.}\)

\(\sqrt{\frac{1}{49}}={\sqrt{1} \over \sqrt{49}}=\frac{1}{7}\text{.}\)

\({9 \over 8\sqrt{2}}={9 \over 8\sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={9\sqrt{2} \over 8⋅2}=\frac{9}{16}\sqrt{2}\text{.}\)

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

\(\sqrt{1\frac{9}{91}}=\sqrt{\frac{100}{91}}={\sqrt{100} \over \sqrt{91}}={10 \over \sqrt{91}}⋅{\sqrt{91} \over \sqrt{91}}={10\sqrt{91} \over 91}=\frac{10}{91}\sqrt{91}\text{.}\)

\(\sqrt{13\frac{1}{2}}=\sqrt{\frac{27}{2}}={\sqrt{27} \over \sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={\sqrt{54} \over 2}=\frac{1}{2}\sqrt{54}=\frac{1}{2}⋅3⋅\sqrt{6}=1\frac{1}{2}\sqrt{6}\text{.}\)

\({21\sqrt{168} \over 3\sqrt{6}}={21 \over 3}⋅{\sqrt{168} \over \sqrt{6}}=7\sqrt{28}=7⋅\sqrt{4}⋅\sqrt{7}=7⋅2⋅\sqrt{7}=14\sqrt{7}\)

\(3\sqrt{5}⋅5\sqrt{10}=15\sqrt{50}=15⋅\sqrt{25}⋅\sqrt{2}=15⋅5⋅\sqrt{2}=75\sqrt{2}\)