Решение:

1. $$\sqrt{18 \cdot 200} = \sqrt{9 \cdot 2 \cdot 100 \cdot 2} = \sqrt{9 \cdot 100 \cdot 4} = 3 \cdot 10 \cdot 2 = 60$$
2. $$\sqrt{36 \cdot 0.4} = \sqrt{36 \cdot \frac{4}{10}} = \sqrt{\frac{144}{10}} = \frac{12}{\sqrt{10}} = \frac{12 \sqrt{10}}{10} = \frac{6 \sqrt{10}}{5}$$
3. $$\sqrt{14.4 \cdot 0.9} = \sqrt{\frac{144}{10} \cdot \frac{9}{10}} = \sqrt{\frac{144 \cdot 9}{100}} = \frac{12 \cdot 3}{10} = \frac{36}{10} = 3.6$$
4. $$\sqrt{13 \cdot 52} = \sqrt{13 \cdot 4 \cdot 13} = \sqrt{13 \cdot 13 \cdot 4} = 13 \cdot 2 = 26$$
5. $$\sqrt{12.5 \cdot 32} = \sqrt{\frac{125}{10} \cdot 32} = \sqrt{\frac{25 \cdot 5 \cdot 16 \cdot 2}{2 \cdot 5}} = \sqrt{25 \cdot 16} = 5 \cdot 4 = 20$$
6. $$\sqrt{108 \cdot 27} = \sqrt{36 \cdot 3 \cdot 9 \cdot 3} = \sqrt{36 \cdot 9 \cdot 9} = 6 \cdot 3 \cdot 3 = 54$$