8. Упростите выражение: 1) (√12 + √27)√3; 2) (√8 − √72)√2; 3) 3√5 + (√75 − √15)√3; 4) (√60 − √45)√5 − 10√3; 5) (√200 + 5√20)√5 − √1000; 6) (√300 − 6√50)√2 − √600.

1. \((\sqrt{12}+\sqrt{27})\sqrt3=(2\sqrt3+3\sqrt3)\sqrt3=5\cdot3=15\).
2. \((\sqrt8-\sqrt{72})\sqrt2=(2\sqrt2-6\sqrt2)\sqrt2=-4\cdot2=-8\).
3. \(3\sqrt5+(\sqrt{75}-\sqrt{15})\sqrt3=3\sqrt5+(5\sqrt3-\sqrt{15})\sqrt3=3\sqrt5+15-3\sqrt5=15\).
4. \((\sqrt{60}-\sqrt{45})\sqrt5-10\sqrt3=(2\sqrt{15}-3\sqrt5)\sqrt5-10\sqrt3=10\sqrt3-15-10\sqrt3=-15\).
5. \((\sqrt{200}+5\sqrt{20})\sqrt5-\sqrt{1000}=(10\sqrt2+10\sqrt5)\sqrt5-10\sqrt{10}=10\sqrt{10}+50-10\sqrt{10}=50\).
6. \((\sqrt{300}-6\sqrt{50})\sqrt2-\sqrt{600}=(10\sqrt3-30\sqrt2)\sqrt2-10\sqrt6=20\sqrt6-60-10\sqrt6=10\sqrt6-60\).

Ответ: 1) 15; 2) −8; 3) 15; 4) −15; 5) 50; 6) \(10\sqrt6-60\).