8. Найдите значение выражения: 1) \(\frac{(7\sqrt{11})^2}{110}\); 2) \(\frac{48}{(2\sqrt6)^2}\); 3) \((\sqrt{23}-4)(\sqrt{23}+4)\); 4) \((\sqrt{15}-\sqrt7)(\sqrt{15}+\sqrt7)\); 5) \((\sqrt{14}-3)^2+6\sqrt{14}\); 6) \(\frac1{4+\sqrt{14}}+\frac1{4-\sqrt{14}}\); 7) \(\frac1{\sqrt{37}-6}-\frac1{\sqrt{37}+6}\).

1. \(\frac{(7\sqrt{11})^2}{110}=\frac{49\cdot11}{110}=\frac{49}{10}\).
2. \(\frac{48}{(2\sqrt6)^2}=\frac{48}{24}=2\).
3. \((\sqrt{23}-4)(\sqrt{23}+4)=23-16=7\).
4. \((\sqrt{15}-\sqrt7)(\sqrt{15}+\sqrt7)=15-7=8\).
5. \((\sqrt{14}-3)^2+6\sqrt{14}=14-6\sqrt{14}+9+6\sqrt{14}=23\).
6. \(\frac1{4+\sqrt{14}}+\frac1{4-\sqrt{14}}=\frac{8}{16-14}=4\).
7. \(\frac1{\sqrt{37}-6}-\frac1{\sqrt{37}+6}=\frac{12}{37-36}=12\).

Ответ: 1) \(\frac{49}{10}\); 2) 2; 3) 7; 4) 8; 5) 23; 6) 4; 7) 12.