Задание 3. Найдите значение выражения. 3) 12/√6; 4) 1/√12; 7) √5/√20; 8) 8/(3√2); 11) (√6+1)/(√6−1); 12) 1/(2√3+3).

1. \(\dfrac{12}{\sqrt6}=\dfrac{12\sqrt6}{6}=2\sqrt6\).
2. \(\dfrac1{\sqrt{12}}=\dfrac1{2\sqrt3}=\dfrac{\sqrt3}{6}\).
3. \(\dfrac{\sqrt5}{\sqrt{20}}=\sqrt{\dfrac5{20}}=\sqrt{\dfrac14}=\dfrac12\).
4. \(\dfrac8{3\sqrt2}=\dfrac{8\sqrt2}{6}=\dfrac{4\sqrt2}{3}\).
5. \(\dfrac{\sqrt6+1}{\sqrt6-1}\cdot\dfrac{\sqrt6+1}{\sqrt6+1}=\dfrac{(\sqrt6+1)^2}{6-1}=\dfrac{7+2\sqrt6}{5}\).
6. \(\dfrac1{2\sqrt3+3}\cdot\dfrac{2\sqrt3-3}{2\sqrt3-3}=\dfrac{2\sqrt3-3}{12-9}=\dfrac{2\sqrt3-3}{3}\).

Ответ: 3) \(2\sqrt6\); 4) \(\frac{\sqrt3}{6}\); 7) \(\frac12\); 8) \(\frac{4\sqrt2}{3}\); 11) \(\frac{7+2\sqrt6}{5}\); 12) \(\frac{2\sqrt3-3}{3}\).