\(\sqrt{75}+\sqrt{300}=\sqrt{25}⋅\sqrt{3}+\sqrt{100}⋅\sqrt{3}=5\sqrt{3}+10\sqrt{3}\text{.}\)

\(5\sqrt{3}+10\sqrt{3}=15\sqrt{3}\text{.}\)

\(\sqrt{700}=\sqrt{100}⋅\sqrt{7}=10\sqrt{7}\text{.}\)

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

\(7\sqrt{18}-6\sqrt{8}=7⋅\sqrt{9}⋅\sqrt{2}-6⋅\sqrt{4}⋅\sqrt{2}\text{.}\)

\(7⋅3⋅\sqrt{2}-6⋅2⋅\sqrt{2}=21\sqrt{2}-12\sqrt{2}=9\sqrt{2}\text{.}\)

\(\sqrt{\frac{1}{36}}={\sqrt{1} \over \sqrt{36}}=\frac{1}{6}\text{.}\)