\(\sqrt{175} = \sqrt{25} ⋅ \sqrt{7} = 5 \sqrt{7} \text{.}\)

\(-4 \sqrt{63} = -4 ⋅ \sqrt{9} ⋅ \sqrt{7} = -4 ⋅ 3 ⋅ \sqrt{7} = -12 \sqrt{7} \text{.}\)

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

\({7 \sqrt{200} \over \sqrt{10}} = 7 ⋅ {\sqrt{200} \over \sqrt{10}} = 7 \sqrt{20} = 7 ⋅ \sqrt{4} ⋅ \sqrt{5} = 7 ⋅ 2 ⋅ \sqrt{5} = 14 \sqrt{5}\)

\(\sqrt{4\frac{3}{4}} = \sqrt{\frac{19}{4}} = {\sqrt{19} \over \sqrt{4}} = {\sqrt{19} \over 2} = \frac{1}{2} \sqrt{19} \text{.}\)