Question

ПОМОГИТЕ ПОДРОБНО РАСПИСАТЬ
$\sqrt{11 + 6 \sqrt{2} } + \sqrt{6 - 4 \sqrt{2} }$

Answer 1

$\sqrt{11 + 6 \sqrt{2} } + \sqrt{6 - 4 \sqrt{2} } = \sqrt{ {(3 + \sqrt{2})}^{2} } + \sqrt{ {2 - \sqrt{2} }^{2} } = 3 + \sqrt{2} + 2 - \sqrt{2} = 3 + 2 = 5.$

Answer 2

$\sqrt{11+6\sqrt2}+\sqrt{6-4\sqrt2}=\\\\=\sqrt{\underbrace {9+2+2\cdot 3\sqrt2}_{a^2+b^2+2ab}}+\sqrt{\underbrace {4+2-2\cdot 2\sqrt2}_{a^2+b^2-2ab}}=\\\\\\=\sqrt{(3+\sqrt2)^2}+\sqrt{(2-\sqrt2)^2}=\\\\=|\underbrace {3+\sqrt2}_{>0}|+|\underbrace {2-\sqrt2}_{>0}|=3+\sqrt2+2-\sqrt2=3+2=5\\\\\\\boxed {\sqrt{a^2}=|a|=\left \{ {{a\; ,\; esli\; a\geq 0\; ,} \atop {-a\; ,\; esli\; a<0\; .}} \right. }$