4. Упростите выражение: 1) 2√3+5/12-3/27; 3) (√5-2)²; 2) (√32-√8)√2; 4) (√6+4√3)(√6-4√3).

1. $$2\sqrt{3}+5\sqrt{12}-3\sqrt{27}=2\sqrt{3}+5\sqrt{4\cdot3}-3\sqrt{9\cdot3}=2\sqrt{3}+5\cdot2\sqrt{3}-3\cdot3\sqrt{3}=2\sqrt{3}+10\sqrt{3}-9\sqrt{3}=3\sqrt{3}$$

2. $$(\sqrt{32}-\sqrt{8})\sqrt{2}=(\sqrt{16\cdot2}-\sqrt{4\cdot2})\sqrt{2}=(4\sqrt{2}-2\sqrt{2})\sqrt{2}=2\sqrt{2}\cdot\sqrt{2}=2\cdot2=4$$

3. $$(\sqrt{5}-2)^2=(\sqrt{5})^2-2\cdot\sqrt{5}\cdot2+2^2=5-4\sqrt{5}+4=9-4\sqrt{5}$$

4. $$(\sqrt{6}+4\sqrt{3})(\sqrt{6}-4\sqrt{3})=(\sqrt{6})^2-(4\sqrt{3})^2=6-16\cdot3=6-48=-42$$

Ответ: 1) $$3\sqrt{3}$$; 2) 4; 3) $$9-4\sqrt{5}$$; 4) -42