6. Найдите значение выражения (√√4-√√2): (√13-√3). V14 Запишите решение и ответ.

1. Упростим выражение: \[\frac{(\sqrt{44} - \sqrt{2})}{\sqrt{14}} : (\sqrt{13\frac{5}{7}} - \sqrt{3\frac{3}{7}}) = \frac{\sqrt{4} \cdot \sqrt{11} - \sqrt{2}}{\sqrt{14}} : (\sqrt{\frac{96}{7}} - \sqrt{\frac{24}{7}})\]
2. Упростим дроби: \[\frac{(2\sqrt{11} - \sqrt{2})}{\sqrt{14}} : (\frac{\sqrt{96} - \sqrt{24}}{\sqrt{7}})\]
3. Разложим на множители: \[\frac{(2\sqrt{11} - \sqrt{2})}{\sqrt{14}} : (\frac{\sqrt{16 \cdot 6} - \sqrt{4 \cdot 6}}{\sqrt{7}}) = \frac{(2\sqrt{11} - \sqrt{2})}{\sqrt{14}} : (\frac{4\sqrt{6} - 2\sqrt{6}}{\sqrt{7}}) = \frac{(2\sqrt{11} - \sqrt{2})}{\sqrt{14}} : (\frac{2\sqrt{6}}{\sqrt{7}})\]
4. Разделим: \[\frac{(2\sqrt{11} - \sqrt{2})}{\sqrt{14}} \cdot (\frac{\sqrt{7}}{2\sqrt{6}}) = \frac{(2\sqrt{11} - \sqrt{2})\sqrt{7}}{\sqrt{14} \cdot 2\sqrt{6}} = \frac{(2\sqrt{11} - \sqrt{2})\sqrt{7}}{2\sqrt{84}} = \frac{(2\sqrt{11} - \sqrt{2})\sqrt{7}}{2\sqrt{4 \cdot 21}} = \frac{(2\sqrt{11} - \sqrt{2})\sqrt{7}}{4\sqrt{21}}\]
5. Упростим: \[\frac{(2\sqrt{11} - \sqrt{2})\sqrt{7}}{4\sqrt{3} \cdot \sqrt{7}} = \frac{2\sqrt{11} - \sqrt{2}}{4\sqrt{3}}\]

Ответ: (2√11 - √2) / (4√3)