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

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

\(\sqrt{28}=\sqrt{4}⋅\sqrt{7}=2\sqrt{7}\text{.}\)

\(-6\sqrt{200}=-6⋅\sqrt{100}⋅\sqrt{2}=-6⋅10⋅\sqrt{2}=-60\sqrt{2}\text{.}\)

\(4\sqrt{27}+6\sqrt{75}=4⋅\sqrt{9}⋅\sqrt{3}+6⋅\sqrt{25}⋅\sqrt{3}\text{.}\)

\(4⋅3⋅\sqrt{3}+6⋅5⋅\sqrt{3}=12\sqrt{3}+30\sqrt{3}=42\sqrt{3}\text{.}\)

\(\sqrt{1\frac{7}{9}}=\sqrt{\frac{16}{9}}={\sqrt{16} \over \sqrt{9}}=\frac{4}{3}=1\frac{1}{3}\text{.}\)

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

\(\sqrt{\frac{41}{100}}={\sqrt{41} \over \sqrt{100}}={\sqrt{41} \over 10}=\frac{1}{10}\sqrt{41}\text{.}\)

\(\sqrt{1\frac{25}{39}}=\sqrt{\frac{64}{39}}={\sqrt{64} \over \sqrt{39}}={8 \over \sqrt{39}}⋅{\sqrt{39} \over \sqrt{39}}={8\sqrt{39} \over 39}=\frac{8}{39}\sqrt{39}\text{.}\)

\(\sqrt{\frac{7}{8}}={\sqrt{7} \over \sqrt{8}}⋅{\sqrt{8} \over \sqrt{8}}={\sqrt{56} \over 8}=\frac{1}{8}\sqrt{56}=\frac{1}{8}⋅2⋅\sqrt{14}=\frac{1}{4}\sqrt{14}\text{.}\)

\({6\sqrt{196} \over 2\sqrt{7}}={6 \over 2}⋅{\sqrt{196} \over \sqrt{7}}=3\sqrt{28}=3⋅\sqrt{4}⋅\sqrt{7}=3⋅2⋅\sqrt{7}=6\sqrt{7}\)

\(2\sqrt{15}⋅3\sqrt{3}=6\sqrt{45}=6⋅\sqrt{9}⋅\sqrt{5}=6⋅3⋅\sqrt{5}=18\sqrt{5}\)