Đáp án:
$E = \sqrt{6 + 2\sqrt{5}} - \sqrt{6 - 2\sqrt{5}}$
$= \sqrt{(\sqrt{5} + 1)^2} - \sqrt{(\sqrt{5} - 1)^2}$
$E = \sqrt{5} + 1 - (\sqrt{5} - 1)$
$E = \sqrt{5} + 1 - \sqrt{5} + 1 = 2$
$F = (3\sqrt{50} - 5\sqrt{18} + 3\sqrt{8}).\sqrt{2}$
$F = (3\sqrt{25.2} - 5\sqrt{9.2} + 3\sqrt{4.2}).\sqrt{2}$
$F = (3.5\sqrt{2} - 5.3\sqrt{2} + 3.2\sqrt{2}).\sqrt{2}$
$F = (15\sqrt{2} - 15\sqrt{2} + 6\sqrt{2}).\sqrt{2} = 6\sqrt{2}.\sqrt{2} = 6.2 = 12$
$G = \sqrt{4 - 2\sqrt{3}} - \dfrac{1}{2}\sqrt{12}$
$G = \sqrt{(\sqrt{3} - 1)^2} - \dfrac{1}{2}.\sqrt{4.3}$
$G = \sqrt{3} - 1 - \dfrac{1}{2}.2.\sqrt{3}$
$G = \sqrt{3} - 1 - \sqrt{3} = - 1$
$H = 2\sqrt{32} - 5\sqrt{27} - 4\sqrt{8} + 3\sqrt{75}$
$H = 2\sqrt{16.2} - 5\sqrt{9.3} - 4\sqrt{4.2} + 3\sqrt{25.3}$
$H = 2.4\sqrt{2} - 5.3\sqrt{3} - 4.2.\sqrt{2} + 3.5\sqrt{3}$
$H = 8\sqrt{2} - 15\sqrt{3} - 8\sqrt{2} + 15\sqrt{3} = 0$
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