\sqrt{2}*\sqrt{6}=\sqrt{2*6}=\sqrt{12}=\sqrt{4*3}=2\sqrt{3}
2\sqrt{3}*\sqrt{18}=2\sqrt{3*18}=2\sqrt{3*2*9}=2*3\sqrt{6}=6\sqrt{6}
7\sqrt{10}*\frac{1}{2}\sqrt{5}=3,5\sqrt{10*5}=3,5\sqrt{50}==3,5\sqrt{2*25}=3,5*5\sqrt{2}=17,5\sqrt{2}
\sqrt{50}+\sqrt{2}=\sqrt{2*25}+\sqrt{2}=5\sqrt{2}+\sqrt{2}=\sqrt{2}(5+1)=6\sqrt{2}
\sqrt{300}-2\sqrt{3}=\sqrt{3*100}-2\sqrt{3}=10\sqrt{3}-2\sqrt{3}=8\sqrt{3}
-2\sqrt{32}-2\sqrt{8}=-2\sqrt{2*16}-2\sqrt{2*4}=-8\sqrt{2}-4\sqrt{2}=-12\sqrt{2}