Вычисляем:

1. $$ sqrt{16 imes 900 imes 169} = sqrt{16} imes sqrt{900} imes sqrt{169} = 4 imes 30 imes 13 = 120 imes 13 = 1560 $$

   Ответ: 1560

2. $$ sqrt{0.25 imes 2.25} = sqrt{0.25} imes sqrt{2.25} = 0.5 imes 1.5 = 0.75 $$

   Ответ: 0.75

3. $$ sqrt{40 imes 490} = sqrt{4 imes 10 imes 49 imes 10} = sqrt{4} imes sqrt{49} imes sqrt{100} = 2 imes 7 imes 10 = 140 $$

   Ответ: 140

4. $$ sqrt{2} imes sqrt{72} = sqrt{2 imes 72} = sqrt{144} = 12 $$

   Ответ: 12

5. $$ sqrt{rac{144}{289}} = rac{sqrt{144}}{sqrt{289}} = rac{12}{17} $$

   Ответ: 12/17

6. $$ sqrt{rac{8}{50}} = sqrt{rac{4}{25}} = rac{sqrt{4}}{sqrt{25}} = rac{2}{5} = 0.4 $$

   Ответ: 0.4

7. $$ sqrt{5^6} = 5^{6/2} = 5^3 = 5 imes 5 imes 5 = 125 $$

   Ответ: 125

8. $$ sqrt{3^4 imes 6^2} = sqrt{3^4} imes sqrt{6^2} = 3^{4/2} imes 6 = 3^2 imes 6 = 9 imes 6 = 54 $$

   Ответ: 54

9. $$ rac{sqrt{12}}{sqrt{75}} + sqrt{36} = sqrt{rac{12}{75}} + 6 = sqrt{rac{4}{25}} + 6 = rac{sqrt{4}}{sqrt{25}} + 6 = rac{2}{5} + 6 = 0.4 + 6 = 6.4 $$

   Ответ: 6.4

10. $$ sqrt{625 imes 4^4} = sqrt{625} imes sqrt{4^4} = 25 imes 4^{4/2} = 25 imes 4^2 = 25 imes 16 = 400 $$

    Ответ: 400