1. \(15\sqrt{20}-4\sqrt{45}+2\sqrt{125}-7\sqrt{80}-\sqrt2\)

Упростим корни: \(\sqrt{20}=2\sqrt5\), \(\sqrt{45}=3\sqrt5\), \(\sqrt{125}=5\sqrt5\), \(\sqrt{80}=4\sqrt5\).

\[15\cdot2\sqrt5-4\cdot3\sqrt5+2\cdot5\sqrt5-7\cdot4\sqrt5-\sqrt2=30\sqrt5-12\sqrt5+10\sqrt5-28\sqrt5-\sqrt2=-\sqrt2.\]

Ответ: \(-\sqrt2\)