1. Вычислите: a) 3\sqrt{1\frac{9}{16}}-1; б) \sqrt{2,5}\cdot\sqrt{10}; в) \frac{\sqrt{0,72}}{\sqrt{8}}; г) \sqrt{3^4\cdot 2^6}.

Пошаговое решение:

1. а) 3\sqrt{1\frac{9}{16}}-1:
   \(\sqrt{1\frac{9}{16}} = \sqrt{\frac{16+9}{16}} = \sqrt{\frac{25}{16}} = \frac{5}{4}\).
   \(3 \cdot \frac{5}{4} - 1 = \frac{15}{4} - 1 = \frac{15-4}{4} = \frac{11}{4} = 2\frac{3}{4}\).
2. б) \sqrt{2,5}\cdot\sqrt{10}:
   \(\sqrt{2,5}\cdot\sqrt{10} = \sqrt{2,5 \cdot 10} = \sqrt{25} = 5\).
3. в) \frac{\sqrt{0,72}}{\sqrt{8}}:
   \(\frac{\sqrt{0,72}}{\sqrt{8}} = \sqrt{\frac{0,72}{8}} = \sqrt{0,09} = 0,3\).
4. г) \sqrt{3^4\cdot 2^6}:
   \(\sqrt{3^4\cdot 2^6} = \sqrt{(3^2)^2 \cdot (2^3)^2} = 3^2 \cdot 2^3 = 9 \cdot 8 = 72\).

Ответ: а) \(2\frac{3}{4}\); б) 5; в) 0,3; г) 72.