Задание 6. Найдите значение выражения: 1) (√21·√14)/√6; 2) (√35·√21)/√15; 3) (√22·√33)/√6; 4) (√65·√13)/√5; 5) (√8·√192)/√24; 6) (√75·√10)/√30.

1. \(\dfrac{\sqrt{21}\cdot\sqrt{14}}{\sqrt6}=\sqrt{\dfrac{21\cdot14}{6}}=\sqrt{49}=7\).
2. \(\dfrac{\sqrt{35}\cdot\sqrt{21}}{\sqrt{15}}=\sqrt{\dfrac{35\cdot21}{15}}=\sqrt{49}=7\).
3. \(\dfrac{\sqrt{22}\cdot\sqrt{33}}{\sqrt6}=\sqrt{\dfrac{22\cdot33}{6}}=\sqrt{121}=11\).
4. \(\dfrac{\sqrt{65}\cdot\sqrt{13}}{\sqrt5}=\sqrt{\dfrac{65\cdot13}{5}}=\sqrt{169}=13\).
5. \(\dfrac{\sqrt8\cdot\sqrt{192}}{\sqrt{24}}=\sqrt{\dfrac{8\cdot192}{24}}=\sqrt{64}=8\).
6. \(\dfrac{\sqrt{75}\cdot\sqrt{10}}{\sqrt{30}}=\sqrt{\dfrac{75\cdot10}{30}}=\sqrt{25}=5\).

Ответ: 1) 7; 2) 7; 3) 11; 4) 13; 5) 8; 6) 5.