$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ a,=2\sqrt{3} +6\sqrt{3} +15\sqrt{3} -36\sqrt{3} =-13\sqrt{3}\\ b,=2\sqrt{3}\left( 3\sqrt{3} +8\sqrt{3} -5\sqrt{3}\right) =2\sqrt{3} .6\sqrt{3} =36\\ c,\ \left( 2\sqrt{2} -\sqrt{3}\right)^{2} =8+3-4\sqrt{6} =11-4\sqrt{6}\\ d,\ \left( 1+\sqrt{3}\right)^{2} -2=1+3+2\sqrt{3} -2=2+2\sqrt{3}\\ e,\ 3-\sqrt{5} +\ 3+\sqrt{5} +2\sqrt{\left( 3+\sqrt{5}\right)\left( 3-\sqrt{5}\right)} =6+2\sqrt{( 9-5)} =10\\ f,\ \sqrt{11} +\sqrt{7} +\sqrt{11} -\sqrt{7} -2\sqrt{\left(\sqrt{11} +\sqrt{7}\right)\left(\sqrt{11} -\sqrt{7}\right)}\\ =2\sqrt{11} -2\sqrt{( 11-7)} =2\sqrt{11} -4\\ Bài\ 2:\\ a,\ \sqrt{\frac{\left(\sqrt{3} +1\right)^{2}}{2}} -\sqrt{\frac{\left(\sqrt{3} -1\right)^{2}}{2}} =\frac{\sqrt{3} +1}{\sqrt{2}} -\frac{\sqrt{3} -1}{\sqrt{2}} =\frac{2}{\sqrt{2}} =\sqrt{2}\\ b,\ \sqrt{\left( 3-2\sqrt{3}\right)^{2}} -\sqrt{3} =2\sqrt{3} -3-\sqrt{3} =\sqrt{3} -3\\ c,\ \sqrt{2}\left(\sqrt{3} +1\right)\left(\sqrt{3} -2\right)\frac{\sqrt{\left(\sqrt{3} +1\right)^{2}}}{\sqrt{2}} =\ \left(\sqrt{3} +1\right)\left(\sqrt{3} -2\right)\left(\sqrt{3} +1\right)\\ =2\left( 2+\sqrt{3}\right)\left(\sqrt{3} -2\right) =2( 3-4) =-2\\ d,\ \left( 4+\sqrt{15}\right)\sqrt{2}\left(\sqrt{5} -\sqrt{3}\right)\frac{\sqrt{\left(\sqrt{5} -\sqrt{3}\right)^{2}}}{\sqrt{2}} =\left( 4+\sqrt{15}\right)\left(\sqrt{5} -\sqrt{3}\right)^{2}\\ =2\left( 4+\sqrt{15}\right)\left( 4-\sqrt{15}\right) =2( 16-15) =2\\ e,\ \sqrt{13-4\sqrt{10} \ } -\sqrt{53+12\sqrt{10}} =\ \sqrt{\left( 2\sqrt{2} -\sqrt{5}\right)^{2} \ } -\sqrt{\left( 2\sqrt{2} +3\sqrt{5}\right)^{2}}\\ =2\sqrt{2} -\sqrt{5} -2\sqrt{2} -3\sqrt{5} =-4\sqrt{5}\\ f,\sqrt{6-2\sqrt{\sqrt{2} +\sqrt{12} +\sqrt{18-8\sqrt{2}}}} =\sqrt{6-2\sqrt{\sqrt{2} +\sqrt{12} +\sqrt{\left( 4-\sqrt{2}\right)^{2}}}}\\ =\sqrt{6-2\sqrt{\sqrt{2} +\sqrt{12} +4-\sqrt{2}}} =\sqrt{6-2\sqrt{2\sqrt{3} +4}} =\sqrt{6-2\sqrt{\left(\sqrt{3} +1\right)^{2}}}\\ =\sqrt{6-2\left(\sqrt{3} +1\right)} =\sqrt{4-2\sqrt{3}} =\sqrt{3} -1 \end{array}$
