Ответ:

  1. \(6\sqrt2+5\sqrt{18}=6\sqrt2+5\cdot3\sqrt2=21\sqrt2\).
  2. \(5\sqrt{75}-2\sqrt{27}=5\cdot5\sqrt3-2\cdot3\sqrt3=19\sqrt3\).
  3. \(\sqrt2+\sqrt{50}-\sqrt{18}=\sqrt2+5\sqrt2-3\sqrt2=3\sqrt2\).
  4. \(3\sqrt{20}+5\sqrt{45}-2\sqrt{80}=3\cdot2\sqrt5+5\cdot3\sqrt5-2\cdot4\sqrt5=17\sqrt5\).
  5. \(2\sqrt{48}+\sqrt{27}+\sqrt{12}=2\cdot4\sqrt3+3\sqrt3+2\sqrt3=13\sqrt3\).
  6. \((\sqrt3-1)(\sqrt3+1)=(\sqrt3)^2-1^2=3-1=2\).

Жауабы: 1) \(21\sqrt2\); 2) \(19\sqrt3\); 3) \(3\sqrt2\); 4) \(17\sqrt5\); 5) \(13\sqrt3\); 6) \(2\).