\(\sqrt{18} = \sqrt{9} ⋅ \sqrt{2} = 3 \sqrt{2} \text{.}\)

\(-2 \sqrt{32} = -2 ⋅ \sqrt{16} ⋅ \sqrt{2} = -2 ⋅ 4 ⋅ \sqrt{2} = -8 \sqrt{2} \text{.}\)

\(\sqrt{1\frac{19}{81}} = \sqrt{\frac{100}{81}} = {\sqrt{100} \over \sqrt{81}} = \frac{10}{9} = 1\frac{1}{9} \text{.}\)

\({42 \sqrt{24} \over 7 \sqrt{3}} = {42 \over 7} ⋅ {\sqrt{24} \over \sqrt{3}} = 6 \sqrt{8} = 6 ⋅ \sqrt{4} ⋅ \sqrt{2} = 6 ⋅ 2 ⋅ \sqrt{2} = 12 \sqrt{2}\)

\(\sqrt{14\frac{3}{4}} = \sqrt{\frac{59}{4}} = {\sqrt{59} \over \sqrt{4}} = {\sqrt{59} \over 2} = \frac{1}{2} \sqrt{59} \text{.}\)