Решение:

1. $$\sqrt{64 \times 36} = \sqrt{64} \times \sqrt{36} = 8 \times 6 = 48$$
2. $$\sqrt{0.04 \times 81} = \sqrt{0.04} \times \sqrt{81} = 0.2 \times 9 = 1.8$$
3. $$\sqrt{324 \times 0.25} = \sqrt{324} \times \sqrt{0.25} = 18 \times 0.5 = 9$$
4. $$\sqrt{0.01 \times 0.04 \times 121} = \sqrt{0.01} \times \sqrt{0.04} \times \sqrt{121} = 0.1 \times 0.2 \times 11 = 0.02 \times 11 = 0.22$$
5. $$\sqrt{\frac{25}{81}} = \frac{\sqrt{25}}{\sqrt{81}} = \frac{5}{9}$$
6. $$\sqrt{5 \frac{1}{16}} = \sqrt{\frac{5 \times 16 + 1}{16}} = \sqrt{\frac{81}{16}} = \frac{\sqrt{81}}{\sqrt{16}} = \frac{9}{4} = 2 \frac{1}{4} = 2.25$$
7. $$\sqrt{\frac{36}{49} \times \frac{196}{225}} = \sqrt{\frac{36}{49}} \times \sqrt{\frac{196}{225}} = \frac{\sqrt{36}}{\sqrt{49}} \times \frac{\sqrt{196}}{\sqrt{225}} = \frac{6}{7} \times \frac{14}{15} = \frac{6 \times 14}{7 \times 15} = \frac{6 \times 2}{15} = \frac{12}{15} = \frac{4}{5} = 0.8$$
8. $$\sqrt{3 \frac{13}{36} \times 12 \frac{24}{25}} = \sqrt{\frac{3 \times 36 + 13}{36} \times \frac{12 \times 25 + 24}{25}} = \sqrt{\frac{121}{36} \times \frac{324}{25}} = \sqrt{\frac{121}{36}} \times \sqrt{\frac{324}{25}} = \frac{\sqrt{121}}{\sqrt{36}} \times \frac{\sqrt{324}}{\sqrt{25}} = \frac{11}{6} \times \frac{18}{5} = \frac{11 \times 18}{6 \times 5} = \frac{11 \times 3}{5} = \frac{33}{5} = 6 \frac{3}{5} = 6.6$$

Ответы:

1. $$\sqrt{64 \times 36} = 48$$
2. $$\sqrt{0.04 \times 81} = 1.8$$
3. $$\sqrt{324 \times 0.25} = 9$$
4. $$\sqrt{0.01 \times 0.04 \times 121} = 0.22$$
5. $$\sqrt{\frac{25}{81}} = \frac{5}{9}$$
6. $$\sqrt{5 \frac{1}{16}} = 2.25$$
7. $$\sqrt{\frac{36}{49} \times \frac{196}{225}} = 0.8$$
8. $$\sqrt{3 \frac{13}{36} \times 12 \frac{24}{25}} = 6.6$$