Вычисляем:

1. a) $$\frac{\sqrt{2}}{\sqrt{32}} = \sqrt{\frac{2}{32}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$$

   Ответ: $$rac{1}{4}$$

2. б) $$\frac{\sqrt{45}}{\sqrt{5}} = \sqrt{\frac{45}{5}} = \sqrt{9} = 3$$

   Ответ: $$3$$

3. a) $$\sqrt{\frac{4}{9}} + \sqrt{\frac{1}{9}} = \frac{\sqrt{4}}{\sqrt{9}} + \frac{\sqrt{1}}{\sqrt{9}} = \frac{2}{3} + \frac{1}{3} = \frac{3}{3} = 1$$

   Ответ: $$1$$

4. б) $$5\sqrt{\frac{1}{25}} + 3\sqrt{\frac{1}{9}} = 5 \cdot \frac{\sqrt{1}}{\sqrt{25}} + 3 \cdot \frac{\sqrt{1}}{\sqrt{9}} = 5 \cdot \frac{1}{5} + 3 \cdot \frac{1}{3} = 1 + 1 = 2$$

   Ответ: $$2$$