\(\sqrt{80}+\sqrt{500}=\sqrt{16}⋅\sqrt{5}+\sqrt{100}⋅\sqrt{5}=4\sqrt{5}+10\sqrt{5}\text{.}\)

\(4\sqrt{5}+10\sqrt{5}=14\sqrt{5}\text{.}\)

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

\(7\sqrt{75}=7⋅\sqrt{25}⋅\sqrt{3}=7⋅5⋅\sqrt{3}=35\sqrt{3}\text{.}\)

\(6\sqrt{75}-5\sqrt{300}=6⋅\sqrt{25}⋅\sqrt{3}-5⋅\sqrt{100}⋅\sqrt{3}\text{.}\)

\(6⋅5⋅\sqrt{3}-5⋅10⋅\sqrt{3}=30\sqrt{3}-50\sqrt{3}=-20\sqrt{3}\text{.}\)

\(\sqrt{\frac{25}{49}}={\sqrt{25} \over \sqrt{49}}=\frac{5}{7}\text{.}\)