Ответ:

  1. \(\sqrt{75\cdot27}=\sqrt{2025}=45\).
  2. \(\sqrt{72\cdot200}=\sqrt{14400}=120\).
  3. \(\sqrt{1.6:14.4}=\sqrt{\frac{1.6}{14.4}}=\sqrt{\frac19}=\frac13\).
  4. \(\sqrt{1590\cdot6.4}=\sqrt{10176}=\sqrt{64\cdot159}=8\sqrt{159}\).

Ответ: 1) 45; 2) 120; 3) \(\frac13\); 4) \(8\sqrt{159}\).