Ответ:

  1. \(7\sqrt{28}-\sqrt{80}-2\sqrt{63}+3\sqrt{45}=14\sqrt7-4\sqrt5-6\sqrt7+9\sqrt5=8\sqrt7+5\sqrt5\).
  2. \(2\sqrt{\frac16}-\sqrt{\frac23}+3\sqrt{\frac1{15}}+4\sqrt{\frac35}=\frac{\sqrt6}{3}-\frac{\sqrt6}{3}+\frac{\sqrt{15}}5+\frac{4\sqrt{15}}5=\sqrt{15}\).
  3. \((\sqrt{18}-3\sqrt2)^2=(3\sqrt2-3\sqrt2)^2=0\).
  4. \((1-\sqrt3)^2(1+\sqrt3)=(1-\sqrt3)(1-3)=2\sqrt3-2\).
  5. \(\frac3{\sqrt5-\sqrt6}-\frac4{\sqrt5+\sqrt6}=-3(\sqrt5+\sqrt6)+4(\sqrt5-\sqrt6)=\sqrt5-7\sqrt6\).
  6. \(\frac2{1+\sqrt3}+\frac3{3-\sqrt5}=\frac{\sqrt3-1}{2}+\frac{9+3\sqrt5}{4}=\frac{7+2\sqrt3+3\sqrt5}{4}\).

Ответ: 1) \(8\sqrt7+5\sqrt5\); 2) \(\sqrt{15}\); 3) \(0\); 4) \(2\sqrt3-2\); 5) \(\sqrt5-7\sqrt6\); 6) \(\frac{7+2\sqrt3+3\sqrt5}{4}\).