Đáp án:

$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 6:a.\ -\sqrt{3} ;\ b.\ 2\\ Bài\ 7:\ a.\ 3+2\sqrt{2} ;\ b.\ 5-2\sqrt{6} ;\ c.\ 2\sqrt{3}\\ BTVN:a.\ 2\sqrt{2} ;\ b.\ 12;\ c.\ 2;\ d.\ 0 \end{array}$

Giải thích các bước giải:

$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 6:\\ a.\ 2\sqrt{12} -3\sqrt{27} +\sqrt{48}\\ =4\sqrt{3} -9\sqrt{3} +4\sqrt{3}\\ =-\sqrt{3}\\ b.\ \left( 3\sqrt{2} -\sqrt{8}\right) .\sqrt{2}\\ =3\sqrt{2} .\sqrt{2} -\sqrt{8.2}\\ =6-4=2\\ Bài\ 7:\\ a.\ \left(\sqrt{2} +1\right)^{2} =2+2\sqrt{2} +1=3+2\sqrt{2}\\ b.\ \left(\sqrt{3} -\sqrt{2}\right)^{2} =3-2\sqrt{6} +2=5-2\sqrt{6}\\ c.\ \sqrt{3+2\sqrt{2}} +\sqrt{5-2\sqrt{6}} +\sqrt{4-2\sqrt{3}}\\ =\sqrt{\left(\sqrt{2} +1\right)^{2}} +\sqrt{\left(\sqrt{3} -\sqrt{2}\right)^{2}} +\sqrt{\left(\sqrt{3} -1\right)^{2}}\\ =\sqrt{2} +1+\sqrt{3} -\sqrt{2} +\sqrt{3} -1=2\sqrt{3}\\ BTVN:\\ a.\ \sqrt{98} -\sqrt{72} +0,5.\sqrt{8}\\ =7\sqrt{2} -6\sqrt{2} +\sqrt{2} =2\sqrt{2}\\ b.\ \left( 3\sqrt{50} -5\sqrt{18} +3\sqrt{8}\right) .\sqrt{2}\\ =\left( 15\sqrt{2} -15\sqrt{2} +6\sqrt{2}\right) .\sqrt{2} =6\sqrt{2.2} =12\\ c.\ \left( 4\sqrt{8} +\sqrt{32} -2\sqrt{18}\right) :3\sqrt{2}\\ =\left( 8\sqrt{2} +4\sqrt{2} -6\sqrt{2}\right) :3\sqrt{2} =6\sqrt{2} :3\sqrt{2} =2\\ d.\ \sqrt{\left(\sqrt{3} -\sqrt{2}\right)^{2}} +\frac{1}{2}\sqrt{8} -\frac{\sqrt{33}}{\sqrt{11}}\\ =\sqrt{3} -\sqrt{2} +\sqrt{2} -\sqrt{3} =0 \end{array}$