Đáp án+Giải thích các bước giải:

$M = \sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}$

$= \sqrt{13+30\sqrt{2+\sqrt{8+2.2\sqrt{2}+1}}}$

$= \sqrt{13+30\sqrt{2+\sqrt{(2\sqrt{2}+1)^2}}}$

$= \sqrt{13+30\sqrt{2+2\sqrt{2}+1}}$

$= \sqrt{13+30\sqrt{(\sqrt{2}+1)^2}}$

$= \sqrt{13+30\sqrt{2}+30}$

$= \sqrt{43+30\sqrt{2}}$

$= \sqrt{25+2.5.3\sqrt{2}+18}$

$= \sqrt{(5+3\sqrt{2})^2}$
$= 5+3\sqrt{2}$

#tuan789