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

\(-3\sqrt{500}=-3⋅\sqrt{100}⋅\sqrt{5}=-3⋅10⋅\sqrt{5}=-30\sqrt{5}\text{.}\)

\(\sqrt{12\frac{1}{4}}=\sqrt{\frac{49}{4}}={\sqrt{49} \over \sqrt{4}}=\frac{7}{2}=3\frac{1}{2}\text{.}\)

\(\sqrt{\frac{32}{81}}={\sqrt{32} \over \sqrt{81}}={\sqrt{32} \over 9}=\frac{1}{9}\sqrt{32}=\frac{1}{9}⋅4⋅\sqrt{2}=\frac{4}{9}\sqrt{2}\text{.}\)