Вариант 4 1. Упростите выражение: a) $$5\sqrt{2}+2\sqrt{32}-\sqrt{98}$$ b) $$(4\sqrt{3}+\sqrt{27})\sqrt{3}$$ v) $$(\sqrt{5}-\sqrt{3})^2$$

a) $$5\sqrt{2}+2\sqrt{32}-\sqrt{98} = 5\sqrt{2}+2\sqrt{16\cdot2}-\sqrt{49\cdot2} = 5\sqrt{2}+2\cdot4\sqrt{2}-7\sqrt{2} = 5\sqrt{2}+8\sqrt{2}-7\sqrt{2} = 6\sqrt{2}$$ Ответ: $$6\sqrt{2}$$ b) $$(4\sqrt{3}+\sqrt{27})\sqrt{3} = (4\sqrt{3}+\sqrt{9\cdot3})\sqrt{3} = (4\sqrt{3}+3\sqrt{3})\sqrt{3} = 7\sqrt{3}\cdot\sqrt{3} = 7\cdot3 = 21$$ Ответ: $$21$$ v) $$(\sqrt{5}-\sqrt{3})^2 = (\sqrt{5})^2 - 2\cdot\sqrt{5}\cdot\sqrt{3} + (\sqrt{3})^2 = 5-2\sqrt{15}+3 = 8-2\sqrt{15}$$ Ответ: $$8-2\sqrt{15}$$