2) √(-3)² ⋅ √36 ⋅ 8 / √32 ⋅ √2 =

Ответ: 9

1. Вычисляем корни: \[\sqrt{(-3)^2} = \sqrt{9} = 3\] \[\sqrt{36} = 6\] \[\sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}\]
2. Подставляем значения: \[\frac{3 \cdot 6 \cdot 8}{4\sqrt{2} \cdot \sqrt{2}} = \frac{3 \cdot 6 \cdot 8}{4 \cdot 2} = \frac{3 \cdot 6 \cdot 8}{8} = 3 \cdot 6 = 18\]
3. Упрощаем: \[\frac{144}{8} = 18\]
4. Если пример выглядит так: √(-3)² ⋅ √36 ⋅ 8 / √32 ⋅ √42 =
   \[\sqrt{(-3)^2} = \sqrt{9} = 3\] \[\sqrt{36} = 6\] \[\sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}\]
   \[\sqrt{42} = \sqrt{42}\]
5. Подставляем значения: \[\frac{3 \cdot 6 \cdot 8}{4\sqrt{2} \cdot \sqrt{42}} = \frac{3 \cdot 6 \cdot 8}{4 \sqrt{84}} = \frac{144}{4\sqrt{84}}=\frac{36}{\sqrt{84}}\]
6. Упрощаем: \[\frac{36}{\sqrt{84}} =\frac{36}{2\sqrt{21}}=\frac{18}{\sqrt{21}} =\frac{18\sqrt{21}}{21} =\frac{6\sqrt{21}}{7} \approx 3.929\]
7. Если пример выглядит так: √(-3)² ⋅ √36 ⋅ √8 / √32 ⋅ √42 =
   \[\sqrt{(-3)^2} = \sqrt{9} = 3\] \[\sqrt{36} = 6\] \[\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}\]
   \[\sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}\]
   \[\sqrt{42} = \sqrt{42}\]
8. Подставляем значения: \[\frac{3 \cdot 6 \cdot 2\sqrt{2}}{4\sqrt{2} \cdot \sqrt{42}} = \frac{36\sqrt{2}}{4 \sqrt{84}} =\frac{9\sqrt{2}}{\sqrt{84}}=\frac{9\sqrt{2}}{2\sqrt{21}}\]
9. Упрощаем: \[\frac{9\sqrt{2}}{2\sqrt{21}} =\frac{9\sqrt{42}}{42} =\frac{3\sqrt{42}}{14} \approx 1.388\]
10. Решим пример, если он выглядит так: √(-3)² ⋅ √36 ⋅ 8 / 32 ⋅ √42 =
    \[\sqrt{(-3)^2} = \sqrt{9} = 3\] \[\sqrt{36} = 6\]
    \[\sqrt{42} = \sqrt{42}\]
11. Подставляем значения: \[\frac{3 \cdot 6 \cdot 8}{32 \cdot \sqrt{42}} = \frac{144}{32 \sqrt{42}} =\frac{9}{2\sqrt{42}}\]
12. Упрощаем: \[\frac{9}{2\sqrt{42}} =\frac{9\sqrt{42}}{84} =\frac{3\sqrt{42}}{28} \approx 0.694\]

Ответ: 9