Đáp án+Giải thích các bước giải:
a,
$11+6\sqrt{2}$
$=11+2.3.\sqrt{2}$
$=9+2.3.\sqrt{2}+2$
$=(3+\sqrt{2})^2(đpcm)$
b,
$\sqrt{11+6\sqrt{2}}+\sqrt{11-6\sqrt{2}}$
$=\sqrt{11+2.3.\sqrt{2}}+\sqrt{11-2.3.\sqrt{2}}$
$=\sqrt{9+2.3.\sqrt{2}+2}+\sqrt{9-2.3.\sqrt{2}+2}$
$=\sqrt{(3+\sqrt{2})^2}+\sqrt{(3-\sqrt{2})^2}$
$=|3+\sqrt{2}|+|3-\sqrt{2}|$
$=3+\sqrt{2}+3-\sqrt{2}$
$=6(đpcm)$