1.217. Упростите выражение: a) √7 + 21/√7; б) (6/√2 + √2)·√2; 6) 18/√3 - 5√3; r) (2/√18 - √2)·√2/3.

Решение:

a) \( \sqrt{7} + \frac{21}{\sqrt{7}} = \sqrt{7} + \frac{21\sqrt{7}}{7} = \sqrt{7} + 3\sqrt{7} = 4\sqrt{7} \)

б) \( (\frac{6}{\sqrt{2}} + \sqrt{2}) \cdot \sqrt{2} = (\frac{6\sqrt{2}}{2} + \sqrt{2}) \cdot \sqrt{2} = (3\sqrt{2} + \sqrt{2}) \cdot \sqrt{2} = 4\sqrt{2} \cdot \sqrt{2} = 4 \cdot 2 = 8 \)

в) \( \frac{18}{\sqrt{3}} - 5\sqrt{3} = \frac{18\sqrt{3}}{3} - 5\sqrt{3} = 6\sqrt{3} - 5\sqrt{3} = \sqrt{3} \)

г) \( (\frac{2}{\sqrt{18}} - \sqrt{2}) \cdot \frac{\sqrt{2}}{3} = (\frac{2}{3\sqrt{2}} - \sqrt{2}) \cdot \frac{\sqrt{2}}{3} = (\frac{2\sqrt{2}}{6} - \sqrt{2}) \cdot \frac{\sqrt{2}}{3} = (\frac{\sqrt{2}}{3} - \sqrt{2}) \cdot \frac{\sqrt{2}}{3} = (\frac{\sqrt{2} - 3\sqrt{2}}{3}) \cdot \frac{\sqrt{2}}{3} = \frac{-2\sqrt{2}}{3} \cdot \frac{\sqrt{2}}{3} = \frac{-2 \cdot 2}{9} = \frac{-4}{9} \)

Ответ: a) 4√7; б) 8; в) √3; г) -4/9.