\(\sqrt{45} = \sqrt{9} ⋅ \sqrt{5} = 3 \sqrt{5} \text{.}\)

\(-6 \sqrt{45} = -6 ⋅ \sqrt{9} ⋅ \sqrt{5} = -6 ⋅ 3 ⋅ \sqrt{5} = -18 \sqrt{5} \text{.}\)

\(\sqrt{\frac{9}{49}} = {\sqrt{9} \over \sqrt{49}} = \frac{3}{7} \text{.}\)

\({72 \sqrt{400} \over 9 \sqrt{10}} = {72 \over 9} ⋅ {\sqrt{400} \over \sqrt{10}} = 8 \sqrt{40} = 8 ⋅ \sqrt{4} ⋅ \sqrt{10} = 8 ⋅ 2 ⋅ \sqrt{10} = 16 \sqrt{10}\)

\(\sqrt{5\frac{7}{16}} = \sqrt{\frac{87}{16}} = {\sqrt{87} \over \sqrt{16}} = {\sqrt{87} \over 4} = \frac{1}{4} \sqrt{87} \text{.}\)