3) Упростите выражение: а) 4√6-√24+√54; б) (√54 - √24) √6; в) (4√3+5)²; г) (3√2 + 2√5) (3√2-2√5).

а) \(4\sqrt{6} - \sqrt{24} + \sqrt{54} = 4\sqrt{6} - \sqrt{4\cdot 6} + \sqrt{9\cdot 6} = 4\sqrt{6} - 2\sqrt{6} + 3\sqrt{6} = (4-2+3)\sqrt{6} = 5\sqrt{6}\) б) \((\sqrt{54} - \sqrt{24}) \cdot \sqrt{6} = (\sqrt{9 \cdot 6} - \sqrt{4 \cdot 6}) \cdot \sqrt{6} = (3\sqrt{6} - 2\sqrt{6})\sqrt{6} = \sqrt{6} \cdot \sqrt{6} = 6\) в) \((4\sqrt{3} + 5)^2 = (4\sqrt{3})^2 + 2 \cdot 4\sqrt{3} \cdot 5 + 5^2 = 16 \cdot 3 + 40\sqrt{3} + 25 = 48 + 40\sqrt{3} + 25 = 73 + 40\sqrt{3}\) г) \((3\sqrt{2} + 2\sqrt{5})(3\sqrt{2} - 2\sqrt{5}) = (3\sqrt{2})^2 - (2\sqrt{5})^2 = 9 \cdot 2 - 4 \cdot 5 = 18 - 20 = -2\)