Решение №2

a) $$8\sqrt{3}-5\sqrt{12}+4\sqrt{75} = 8\sqrt{3}-5\sqrt{4\cdot3}+4\sqrt{25\cdot3} = 8\sqrt{3}-5\cdot2\sqrt{3}+4\cdot5\sqrt{3} = 8\sqrt{3}-10\sqrt{3}+20\sqrt{3} = 18\sqrt{3}$$

б) $$(\sqrt{20}+\sqrt{80})\cdot\sqrt{5} = (\sqrt{4\cdot5}+\sqrt{16\cdot5})\cdot\sqrt{5} = (2\sqrt{5}+4\sqrt{5})\cdot\sqrt{5} = 6\sqrt{5}\cdot\sqrt{5} = 6\cdot5 = 30$$

в) $$(2\sqrt{7} + 3)^2 = (2\sqrt{7})^2 + 2\cdot2\sqrt{7}\cdot3 + 3^2 = 4\cdot7 + 12\sqrt{7} + 9 = 28 + 12\sqrt{7} + 9 = 37 + 12\sqrt{7}$$

г) $$(7\sqrt{2}+3\sqrt{3})(7\sqrt{2}-3\sqrt{3}) = (7\sqrt{2})^2 - (3\sqrt{3})^2 = 49\cdot2 - 9\cdot3 = 98 - 27 = 71$$