4. Упростите выражение: 1) 5√2-4√8+3√32; 2) (√75-√12)√3; 3) (√7-3)²; 4) (√5+2√2)(√5-2√2).

1) $$5\sqrt{2} - 4\sqrt{8} + 3\sqrt{32}$$:

$$5\sqrt{2} - 4\sqrt{4\cdot2} + 3\sqrt{16\cdot2} = 5\sqrt{2} - 4\cdot2\sqrt{2} + 3\cdot4\sqrt{2} = 5\sqrt{2} - 8\sqrt{2} + 12\sqrt{2} = (5 - 8 + 12)\sqrt{2} = 9\sqrt{2}$$

Ответ: $$9\sqrt{2}$$

2) $$(\sqrt{75} - \sqrt{12})\sqrt{3}$$:

$$(\sqrt{25\cdot3} - \sqrt{4\cdot3})\sqrt{3} = (5\sqrt{3} - 2\sqrt{3})\sqrt{3} = 3\sqrt{3} \cdot \sqrt{3} = 3 \cdot 3 = 9$$

Ответ: 9

3) $$(\sqrt{7} - 3)^2$$:

$$(\sqrt{7} - 3)^2 = (\sqrt{7})^2 - 2\cdot3\sqrt{7} + 3^2 = 7 - 6\sqrt{7} + 9 = 16 - 6\sqrt{7}$$

Ответ: $$16 - 6\sqrt{7}$$

4) $$(\sqrt{5} + 2\sqrt{2})(\sqrt{5} - 2\sqrt{2})$$:

$$(\sqrt{5} + 2\sqrt{2})(\sqrt{5} - 2\sqrt{2}) = (\sqrt{5})^2 - (2\sqrt{2})^2 = 5 - 4 \cdot 2 = 5 - 8 = -3$$

Ответ: -3