Đáp án: $-2\sqrt{6}$
Giải thích các bước giải:
$\sqrt{49-5\sqrt{96}}-\sqrt{49+5\sqrt{96}}+2\sqrt{6}$
$=\sqrt{49-5\sqrt{96}}-\sqrt{49+5\sqrt{96}}+2\sqrt{6}$
$=\sqrt{25-2.5.2\sqrt{6}+24}-\sqrt{25+2.5.2\sqrt{6}+24}+2\sqrt{6}$
$=\sqrt{(5-2\sqrt{6})^2}-\sqrt{(5+2\sqrt{6})^2}+2\sqrt{6}$
$=|5-2\sqrt{6}|-|5+2\sqrt{6}|+2\sqrt{6}$
$=(5-2\sqrt{6})-(5+2\sqrt{6})+2\sqrt{6}$
$=5-2\sqrt{6}-5-2\sqrt{6}+2\sqrt{6}$
$=-2\sqrt{6}$
