\(\sqrt{45} + \sqrt{80} = \sqrt{9} ⋅ \sqrt{5} + \sqrt{16} ⋅ \sqrt{5} = 3 \sqrt{5} + 4 \sqrt{5} \text{.}\)

\(3 \sqrt{5} + 4 \sqrt{5} = 7 \sqrt{5} \text{.}\)

\(\sqrt{80} = \sqrt{16} ⋅ \sqrt{5} = 4 \sqrt{5} \text{.}\)

\(-6 \sqrt{50} = -6 ⋅ \sqrt{25} ⋅ \sqrt{2} = -6 ⋅ 5 ⋅ \sqrt{2} = -30 \sqrt{2} \text{.}\)

\(2 \sqrt{27} + 3 \sqrt{48} = 2 ⋅ \sqrt{9} ⋅ \sqrt{3} + 3 ⋅ \sqrt{16} ⋅ \sqrt{3} \text{.}\)

\(2 ⋅ 3 ⋅ \sqrt{3} + 3 ⋅ 4 ⋅ \sqrt{3} = 6 \sqrt{3} + 12 \sqrt{3} = 18 \sqrt{3} \text{.}\)

\(\sqrt{\frac{9}{16}} = {\sqrt{9} \over \sqrt{16}} = \frac{3}{4} \text{.}\)

\({7 \over 2 \sqrt{3}} = {7 \over 2 \sqrt{3}} ⋅ {\sqrt{3} \over \sqrt{3}} = {7 \sqrt{3} \over 2 ⋅ 3} = 1\frac{1}{6} \sqrt{3} \text{.}\)

\(\sqrt{\frac{67}{81}} = {\sqrt{67} \over \sqrt{81}} = {\sqrt{67} \over 9} = \frac{1}{9} \sqrt{67} \text{.}\)

\(\sqrt{1\frac{19}{45}} = \sqrt{\frac{64}{45}} = {\sqrt{64} \over \sqrt{45}} = {8 \over \sqrt{45}} ⋅ {\sqrt{45} \over \sqrt{45}} = {8 \sqrt{45} \over 45} = \frac{8}{45} \sqrt{45} = \frac{8}{45} ⋅ 3 ⋅ \sqrt{5} = \frac{8}{15} \sqrt{5} \text{.}\)

\(\sqrt{\frac{2}{27}} = {\sqrt{2} \over \sqrt{27}} ⋅ {\sqrt{27} \over \sqrt{27}} = {\sqrt{54} \over 27} = \frac{1}{27} \sqrt{54} = \frac{1}{27} ⋅ 3 ⋅ \sqrt{6} = \frac{1}{9} \sqrt{6} \text{.}\)

\({7 \sqrt{196} \over \sqrt{7}} = 7 ⋅ {\sqrt{196} \over \sqrt{7}} = 7 \sqrt{28} = 7 ⋅ \sqrt{4} ⋅ \sqrt{7} = 7 ⋅ 2 ⋅ \sqrt{7} = 14 \sqrt{7}\)

\(2 \sqrt{5} ⋅ 3 \sqrt{10} = 6 \sqrt{50} = 6 ⋅ \sqrt{25} ⋅ \sqrt{2} = 6 ⋅ 5 ⋅ \sqrt{2} = 30 \sqrt{2}\)