TRẢ LỜI

1. Giải đáp:

   $59. =\dfrac{\sqrt{5}+\sqrt{7}}{\sqrt{2}}\\ 60. =\dfrac{3-\sqrt{5}}{\sqrt{2}}\\ 61.  =\dfrac{3\sqrt{5}+1}{\sqrt{2}}\\ 62.\dfrac{\sqrt{11}-\sqrt{3}}{\sqrt{2}}\\ 63.\dfrac{\sqrt{11}+\sqrt{5}}{\sqrt{2}} $

   Lời giải và giải thích chi tiết:

   $59. \sqrt{6+\sqrt{35}}\\ =\dfrac{\sqrt{2}.\sqrt{6+\sqrt{35}}}{\sqrt{2}}\\ =\dfrac{\sqrt{12+2\sqrt{35}}}{\sqrt{2}}\\ =\dfrac{\sqrt{5+2.\sqrt{5}.\sqrt{7}+7}}{\sqrt{2}}\\ =\dfrac{\sqrt{(\sqrt{5}+\sqrt{7})^2}}{\sqrt{2}}\\ =\dfrac{\sqrt{5}+\sqrt{7}}{\sqrt{2}}\\ 60. \sqrt{7-3\sqrt{5}}\\ =\dfrac{\sqrt{2}.\sqrt{7-3\sqrt{5}}}{\sqrt{2}}\\ =\dfrac{\sqrt{14-2.3\sqrt{5}}}{\sqrt{2}}\\ =\dfrac{\sqrt{9-2.3.\sqrt{5}+5}}{\sqrt{2}}\\ =\dfrac{\sqrt{(3-\sqrt{5})^2}}{\sqrt{2}}\\ =\dfrac{3-\sqrt{5}}{\sqrt{2}}\\ 61. \sqrt{23+3\sqrt{5}}\\ =\dfrac{\sqrt{2}.\sqrt{23+3\sqrt{5}}}{\sqrt{2}}\\ =\dfrac{\sqrt{46+2.3\sqrt{5}}}{\sqrt{2}}\\ =\dfrac{\sqrt{45+2.3\sqrt{5}.1+1}}{\sqrt{2}}\\ =\dfrac{\sqrt{(3\sqrt{5}+1)^2}}{\sqrt{2}}\\ =\dfrac{3\sqrt{5}+1}{\sqrt{2}}\\ 62.\sqrt{7-\sqrt{33}}\\ =\dfrac{\sqrt{2}.\sqrt{7-\sqrt{33}}}{\sqrt{2}}\\ =\dfrac{\sqrt{14-2\sqrt{33}}}{\sqrt{2}}\\ =\dfrac{\sqrt{11-2.\sqrt{3}.\sqrt{11}+3}}{\sqrt{2}}\\ =\dfrac{\sqrt{(\sqrt{11}-\sqrt{3})^2}}{\sqrt{2}}\\ =\dfrac{\sqrt{11}-\sqrt{3}}{\sqrt{2}}\\ 63.\sqrt{8+\sqrt{55}}\\ =\dfrac{\sqrt{2}.\sqrt{8+\sqrt{55}}}{\sqrt{2}}\\ =\dfrac{\sqrt{16+2\sqrt{55}}}{\sqrt{2}}\\ =\dfrac{\sqrt{11+2.\sqrt{5}.\sqrt{11}+5}}{\sqrt{2}}\\ =\dfrac{\sqrt{(\sqrt{11}+\sqrt{5})^2}}{\sqrt{2}}\\ =\dfrac{\sqrt{11}+\sqrt{5}}{\sqrt{2}}$

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