\(\sqrt{200}=\sqrt{100}⋅\sqrt{2}=10\sqrt{2}\text{.}\)

\(-3\sqrt{20}=-3⋅\sqrt{4}⋅\sqrt{5}=-3⋅2⋅\sqrt{5}=-6\sqrt{5}\text{.}\)

\(\sqrt{2\frac{1}{4}}=\sqrt{\frac{9}{4}}={\sqrt{9} \over \sqrt{4}}=\frac{3}{2}=1\frac{1}{2}\text{.}\)

\({54\sqrt{160} \over 6\sqrt{8}}={54 \over 6}⋅{\sqrt{160} \over \sqrt{8}}=9\sqrt{20}=9⋅\sqrt{4}⋅\sqrt{5}=9⋅2⋅\sqrt{5}=18\sqrt{5}\)