Ты просишь упростить алгебраические выражения с радикалами (квадратными корнями).

а) $2\sqrt{2}+3\sqrt{2} = (2+3)\sqrt{2} = 5\sqrt{2}$. б) $2\sqrt{8}-3\sqrt{2} = 2\sqrt{4*2} - 3\sqrt{2} = 2*2\sqrt{2} - 3\sqrt{2} = 4\sqrt{2} - 3\sqrt{2} = \sqrt{2}$. в) $\sqrt{a} - 5\sqrt{a} = (1-5)\sqrt{a} = -4\sqrt{a}$. г) $a\sqrt{x} - 3\sqrt{x} = (a-3)\sqrt{x}$. д) $2\sqrt{a} + 3\sqrt{a} - \sqrt{4a} = 2\sqrt{a} + 3\sqrt{a} - \sqrt{4}\sqrt{a} = 2\sqrt{a} + 3\sqrt{a} - 2\sqrt{a} = (2+3-2)\sqrt{a} = 3\sqrt{a}$. е) $\sqrt{2} + 3\sqrt{32} + \frac{1}{2}\sqrt{128} - 6\sqrt{18} = \sqrt{2} + 3\sqrt{16*2} + \frac{1}{2}\sqrt{64*2} - 6\sqrt{9*2} = \sqrt{2} + 3*4\sqrt{2} + \frac{1}{2}*8\sqrt{2} - 6*3\sqrt{2} = \sqrt{2} + 12\sqrt{2} + 4\sqrt{2} - 18\sqrt{2} = (1+12+4-18)\sqrt{2} = -\sqrt{2}$. ж) $(8+3\sqrt{5}) (2-\sqrt{5}) = 8*2 + 3\sqrt{5}*2 - 8*\sqrt{5} - 3\sqrt{5}*\sqrt{5} = 16 + 6\sqrt{5} - 8\sqrt{5} - 3*5 = 16 - 15 + (6-8)\sqrt{5} = 1 - 2\sqrt{5}$. з) $(3\sqrt{8} + \sqrt{18} + \sqrt{50} - 2\sqrt{72}) \cdot \sqrt{2} = (3\sqrt{4*2} + \sqrt{9*2} + \sqrt{25*2} - 2\sqrt{36*2}) \cdot \sqrt{2} = (3*2\sqrt{2} + 3\sqrt{2} + 5\sqrt{2} - 2*6\sqrt{2}) \cdot \sqrt{2} = (6\sqrt{2} + 3\sqrt{2} + 5\sqrt{2} - 12\sqrt{2}) \cdot \sqrt{2} = (6+3+5-12)\sqrt{2} * \sqrt{2} = 2\sqrt{2} * \sqrt{2} = 2*2 = 4$. и) $(3-\sqrt{2}) (2+3\sqrt{2}) = 3*2 - \sqrt{2}*2 + 3*3\sqrt{2} - \sqrt{2}*3\sqrt{2} = 6 - 2\sqrt{2} + 9\sqrt{2} - 3*2 = 6 - 6 + (9-2)\sqrt{2} = 7\sqrt{2}$. к) $(7\sqrt{2}-5\sqrt{6}-3\sqrt{8}+4\sqrt{20})\cdot 3\sqrt{2} = (7\sqrt{2}-5\sqrt{6}-3\sqrt{4*2}+4\sqrt{4*5})\cdot 3\sqrt{2} = (7\sqrt{2}-5\sqrt{6}-3*2\sqrt{2}+4*2\sqrt{5})\cdot 3\sqrt{2} = (7\sqrt{2}-5\sqrt{6}-6\sqrt{2}+8\sqrt{5})\cdot 3\sqrt{2} = (7\sqrt{2}-6\sqrt{2}-5\sqrt{6}+8\sqrt{5})\cdot 3\sqrt{2} = (\sqrt{2}-5\sqrt{6}+8\sqrt{5})\cdot 3\sqrt{2} = \sqrt{2}*3\sqrt{2} - 5\sqrt{6}*3\sqrt{2} + 8\sqrt{5}*3\sqrt{2} = 3*2 - 15\sqrt{12} + 24\sqrt{10} = 6 - 15\sqrt{4*3} + 24\sqrt{10} = 6 - 15*2\sqrt{3} + 24\sqrt{10} = 6 - 30\sqrt{3} + 24\sqrt{10}$. л) $(2\sqrt{6}+5\sqrt{3}-7\sqrt{2}) (\sqrt{6} - 2\sqrt{3}+4\sqrt{2}) = 2\sqrt{6}*\sqrt{6} + 5\sqrt{3}*\sqrt{6} - 7\sqrt{2}*\sqrt{6} - 2\sqrt{6}*2\sqrt{3} - 5\sqrt{3}*2\sqrt{3} + 7\sqrt{2}*2\sqrt{3} + 2\sqrt{6}*4\sqrt{2} + 5\sqrt{3}*4\sqrt{2} - 7\sqrt{2}*4\sqrt{2} = 2*6 + 5\sqrt{18} - 7\sqrt{12} - 4\sqrt{18} - 10*3 + 14\sqrt{6} + 8\sqrt{12} + 20\sqrt{6} - 28*2 = 12 - 30 - 56 + (5-4)\sqrt{18} + (8-7)\sqrt{12} + (14+20)\sqrt{6} = -74 + \sqrt{9*2} + \sqrt{4*3} + 34\sqrt{6} = -74 + 3\sqrt{2} + 2\sqrt{3} + 34\sqrt{6}$. м) $(\sqrt{12}-1) (\sqrt{12}+1) = \sqrt{12}*\sqrt{12} - 1*1 = 12 - 1 = 11$. н) $(7-\sqrt{3}) (\sqrt{3}+7) = 7*\sqrt{3} - \sqrt{3}*\sqrt{3} + 7*7 - \sqrt{3}*7 = 7\sqrt{3} - 3 + 49 - 7\sqrt{3} = 46$. о) $(\sqrt{20}-3) (3+2\sqrt{5}) = \sqrt{20}*3 - 3*3 + \sqrt{20}*2\sqrt{5} - 3*2\sqrt{5} = 3\sqrt{4*5} - 9 + 2\sqrt{4*5}*\sqrt{5} - 6\sqrt{5} = 3*2\sqrt{5} - 9 + 2*2*5 - 6\sqrt{5} = 6\sqrt{5} - 9 + 20 - 6\sqrt{5} = 11$. Все примеры упростил. Если что-то непонятно, спрашивай!