a) (3√50-2√18)√32; B) (5√27+4√12)√75; д) √6:(√150-√96); 6) (8√28-3√63):√; г) (6√44+√99):√1; e) √8·(3√32+√128)

Решение:

а) \( (3\sqrt{50} - 2\sqrt{18}) \cdot \sqrt{32} \)

• \( \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} \)
• \( \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \)
• \( \sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2} \)
• \( (3 \cdot 5\sqrt{2} - 2 \cdot 3\sqrt{2}) \cdot 4\sqrt{2} = (15\sqrt{2} - 6\sqrt{2}) \cdot 4\sqrt{2} = 9\sqrt{2} \cdot 4\sqrt{2} = 36 \cdot 2 = 72 \)

б) \( (5\sqrt{27} + 4\sqrt{12}) \cdot \sqrt{75} \)

• \( \sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3} \)
• \( \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3} \)
• \( \sqrt{75} = \sqrt{25 \cdot 3} = 5\sqrt{3} \)
• \( (5 \cdot 3\sqrt{3} + 4 \cdot 2\sqrt{3}) \cdot 5\sqrt{3} = (15\sqrt{3} + 8\sqrt{3}) \cdot 5\sqrt{3} = 23\sqrt{3} \cdot 5\sqrt{3} = 115 \cdot 3 = 345 \)

г) \( \sqrt{6} : (\sqrt{150} - \sqrt{96}) \)

• \( \sqrt{150} = \sqrt{25 \cdot 6} = 5\sqrt{6} \)
• \( \sqrt{96} = \sqrt{16 \cdot 6} = 4\sqrt{6} \)
• \( \sqrt{6} : (5\sqrt{6} - 4\sqrt{6}) = \sqrt{6} : \sqrt{6} = 1 \)

д) \( 6\sqrt{44} + \sqrt{99} \)

• \( \sqrt{44} = \sqrt{4 \cdot 11} = 2\sqrt{11} \)
• \( \sqrt{99} = \sqrt{9 \cdot 11} = 3\sqrt{11} \)
• \( 6 \cdot 2\sqrt{11} + 3\sqrt{11} = 12\sqrt{11} + 3\sqrt{11} = 15\sqrt{11} \)

е) \( \sqrt{8} \cdot (3\sqrt{32} + \sqrt{128}) \)

• \( \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} \)
• \( \sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2} \)
• \( \sqrt{128} = \sqrt{64 \cdot 2} = 8\sqrt{2} \)
• \( 2\sqrt{2} \cdot (3 \cdot 4\sqrt{2} + 8\sqrt{2}) = 2\sqrt{2} \cdot (12\sqrt{2} + 8\sqrt{2}) = 2\sqrt{2} \cdot 20\sqrt{2} = 40 \cdot 2 = 80 \)

6) \( (8\sqrt{28} - 3\sqrt{63}) : \sqrt{7} \)

• \( \sqrt{28} = \sqrt{4 \cdot 7} = 2\sqrt{7} \)
• \( \sqrt{63} = \sqrt{9 \cdot 7} = 3\sqrt{7} \)
• \( (8 \cdot 2\sqrt{7} - 3 \cdot 3\sqrt{7}) : \sqrt{7} = (16\sqrt{7} - 9\sqrt{7}) : \sqrt{7} = 7\sqrt{7} : \sqrt{7} = 7 \)

Ответ: а) 72; б) 345; г) 1; д) 15√11; е) 80; 6) 7.