Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} 46.\sqrt{45} -1\\ 47.\ 2\sqrt{5} +3\\ 48.\sqrt{3} +2\sqrt{6}\\ 49.5-2\sqrt{6}\\ 50.4\sqrt{6} -\sqrt{2} \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} 46.\sqrt{46-6\sqrt{5}} =\sqrt{\left(\sqrt{45} -1\right)^{2}} =\sqrt{45} -1\\ 47.\ \sqrt{29+12\sqrt{5}} =\sqrt{\left( 2\sqrt{5} +3\right)^{2}} =2\sqrt{5} +3\\ 48.\ \sqrt{27+12\sqrt{2}} =\sqrt{3}\sqrt{9+4\sqrt{2}} =\sqrt{3}\sqrt{\left( 1+2\sqrt{2}\right)^{2}} =\sqrt{3} +2\sqrt{6}\\ 49.\sqrt{49-20\sqrt{6}} =\sqrt{\left( 2\sqrt{6} -5\right)^{2}} =5-2\sqrt{6}\\ 50.\sqrt{98-16\sqrt{3}} =\sqrt{2}\sqrt{49-8\sqrt{3}} =\sqrt{2}\sqrt{\left(\sqrt{48} -1\right)^{2}}\\ =\sqrt{2}\left(\sqrt{48} -1\right) =4\sqrt{6} -\sqrt{2} \end{array}$
