Đáp án:
Giải thích các bước giải:
a)
$\sqrt{3 + 2\sqrt{2}} = \sqrt{2 + 2\sqrt{2} + 1} = \sqrt{(\sqrt{2} + 1)²} = \sqrt{2} + 1$
b)
$\sqrt{4 - 2\sqrt{3}} = \sqrt{3 - 2\sqrt{3} + 1} = \sqrt{(\sqrt{3} - 1)²} = \sqrt{3} - 1$
c)
$\sqrt{11 - 2\sqrt{30}} = \sqrt{6 - 2\sqrt{6}\sqrt{5} + 5} = \sqrt{(\sqrt{6} - \sqrt{5})²} = \sqrt{6} - \sqrt{5} $
d)
$\sqrt{11 - 4\sqrt{7}} = \sqrt{7 - 2.2\sqrt{7} + 4} = \sqrt{(\sqrt{7} - 2)²} = \sqrt{7} - 2 $
e)
$\sqrt{7 + 2\sqrt{10}} = \sqrt{5 + 2\sqrt{5}\sqrt{2} + 2} = \sqrt{(\sqrt{5} + \sqrt{2})²} = \sqrt{5} - \sqrt{2} $
f)
$\sqrt{14 - 2\sqrt{33}} = \sqrt{11 - 2\sqrt{11}\sqrt{3} + 3} = \sqrt{(\sqrt{11} - \sqrt{3})²} = \sqrt{11} - \sqrt{3} $
g)
$\sqrt{17 - 12\sqrt{2}} = \sqrt{9 - 2.3.\sqrt{8} + 8} = \sqrt{(3 - \sqrt{8})²} = 3 - \sqrt{8} $
h)
$\sqrt{25 + 4\sqrt{6}} = \sqrt{24 - 2\sqrt{24} + 1} = \sqrt{(\sqrt{24} - 1)²} = \sqrt{24} - 1 $
k)
$\sqrt{21 - 6\sqrt{6}} = \sqrt{18 - 2.(3\sqrt{2})\sqrt{3} + 3} = \sqrt{(3\sqrt{2} - \sqrt{3})²} = 3\sqrt{2} - \sqrt{3} $
