1) \(\frac{\sqrt{21} \cdot \sqrt{14}}{\sqrt{6}}\)

1. \(\frac{\sqrt{3 \cdot 7} \cdot \sqrt{2 \cdot 7}}{\sqrt{2 \cdot 3}}\) = \(\frac{\sqrt{3} \cdot \sqrt{7} \cdot \sqrt{2} \cdot \sqrt{7}}{\sqrt{2} \cdot \sqrt{3}}\).
2. \(\sqrt{7}\) \(\cdot\) \(\sqrt{7}\) = 7.
3. \(\text{Ответ: }\) 7.