7: \(\dfrac{\left(\sqrt{12}+\sqrt{75}+\sqrt{27}\right)}{\sqrt{15}}\)
\(=\dfrac{2\sqrt{3}+5\sqrt{3}+3\sqrt{3}}{\sqrt{15}}=\dfrac{10\sqrt{3}}{\sqrt{15}}=\dfrac{10}{\sqrt{5}}=2\sqrt{5}\)
10: \(\sqrt{12}\left(5\sqrt{3}-\sqrt{27}\right)\)
\(=2\sqrt{3}\left(5\sqrt{3}-3\sqrt{3}\right)=2\sqrt{3}\cdot2\sqrt{3}=12\)
15: \(\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right)\cdot\sqrt{7}+\sqrt{84}\)
\(=\left(2\sqrt{7}+\sqrt{7}-2\sqrt{3}\right)\cdot\sqrt{7}+2\sqrt{21}\)
\(=\left(3\sqrt{7}-2\sqrt{3}\right)\cdot\sqrt{7}+2\sqrt{21}=21-2\sqrt{21}+2\sqrt{21}=21\)
16: \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\cdot\sqrt{7}+7\sqrt{8}\)
\(=\left(2\sqrt{7}+\sqrt{7}-2\sqrt{14}\right)\cdot\sqrt{7}+7\sqrt{8}\)
\(=\left(3\sqrt{7}-2\sqrt{14}\right)\cdot\sqrt{7}+7\cdot2\sqrt{2}\)
\(=21-2\sqrt{98}+14\sqrt{2}=21\)
17: \(\left(\sqrt{12}-2\sqrt{18}+5\sqrt{3}\right)\cdot\sqrt{3}+5\sqrt{6}\)
\(=\left(2\sqrt{3}-2\cdot3\sqrt{2}+5\sqrt{3}\right)\cdot\sqrt{3}+5\sqrt{6}\)
\(=\left(7\sqrt{3}-6\sqrt{2}\right)\cdot\sqrt{3}+5\sqrt{6}\)
\(=21-6\sqrt{6}+5\sqrt{6}=21-\sqrt{6}\)
18: \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\cdot\sqrt{11}+3\sqrt{22}\)
\(=\left(3\sqrt{11}-3\sqrt{2}-\sqrt{11}\right)\cdot\sqrt{11}+3\sqrt{22}\)
\(=\left(2\sqrt{11}-3\sqrt{2}\right)\cdot\sqrt{11}+3\sqrt{22}\)
\(=22-3\sqrt{22}+3\sqrt{22}=22\)
