$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 14:\\ \\ a.=\frac{\left( 10+2\sqrt{10}\right)\left(\sqrt{5} -\sqrt{2}\right)}{\left(\sqrt{5} -\sqrt{2}\right)\left(\sqrt{5} +\sqrt{2}\right)} =\frac{6\sqrt{5}}{5-2} =2\sqrt{5}\\ b.=\frac{\left( 2\sqrt{8} -\sqrt{12}\right)\left(\sqrt{18} -\sqrt{48}\right)}{\left(\sqrt{18} -\sqrt{48}\right)\left(\sqrt{18} +\sqrt{48}\right)} =\frac{48-22\sqrt{6}}{18-48} =\frac{48-22\sqrt{6}}{-30}\\ c.\ =\frac{\sqrt{2}\left(\sqrt{5} +\sqrt{3}\right)}{\left(\sqrt{5} +\sqrt{3}\right)\left(\sqrt{5} -\sqrt{3}\right)} =\frac{\sqrt{2}\left(\sqrt{5} +\sqrt{3}\right)}{2}\\ d.\ \sqrt{\frac{\left( 2-\sqrt{3}\right)^{2}}{4-3}} =\ \sqrt{\frac{\left( 2-\sqrt{3}\right)^{2}}{1}} =2-\sqrt{3}\\ Bài\ 15:\\ a.\ \left[\frac{15\left(\sqrt{6} -1\right)}{\left(\sqrt{6} -1\right)\left(\sqrt{6} +1\right)} +\frac{4\left(\sqrt{6} +2\right)}{\left(\sqrt{6} +2\right)\left(\sqrt{6} -2\right)} -\frac{12\left(\sqrt{6} +3\right)}{\left( 3-\sqrt{6}\right)\left( 3+\sqrt{6}\right)}\right]\left(\sqrt{6} +11\right)\\ =\left[\frac{15\sqrt{6} -15}{6-1} +\frac{4\sqrt{6} +8}{6-4} -\frac{12\sqrt{6} +36}{9-6}\right]\left(\sqrt{6} +11\right)\\ =\left[\frac{15\sqrt{6} -15}{5} +\frac{4\sqrt{6} +8}{2} -\frac{12\sqrt{6} +36}{3}\right]\left(\sqrt{6} +11\right)\\ =\left(\sqrt{6} -11\right)\left(\sqrt{6} +11\right)\\ =6-121=-115\\ b.\ \frac{3+\sqrt{5}}{9-5} -\frac{\sqrt{5} +1}{5-1} =\ \frac{3+\sqrt{5}}{4} -\frac{\sqrt{5} +1}{4} =\frac{2}{4} =\frac{1}{2}\\ c.\ =\frac{\sqrt{5} -1}{\left(\sqrt{5} +1\right)\left(\sqrt{5} -1\right)} +\frac{\sqrt{5} +2}{\left(\sqrt{5} +2\right)\left(\sqrt{5} -2\right)} -\frac{\sqrt{5} +3}{\left( 3-\sqrt{5}\right)\left(\sqrt{5} +3\right)} -\sqrt{5}\\ =\frac{\sqrt{5} -1}{5-1} +\frac{\sqrt{5} +2}{5-4} -\frac{\sqrt{5} +3}{9-5} -\sqrt{5}\\ =\frac{\sqrt{5} -1}{4} +\frac{\sqrt{5} +2}{1} -\frac{\sqrt{5} +3}{4} -\sqrt{5}\\ =\frac{-4}{4} +2=-1+2=1\\ d.\ =\frac{5-3\sqrt{2}}{\left( 5+3\sqrt{2}\right)\left( 5-3\sqrt{2}\right)} +\frac{5+3\sqrt{2}}{\left( 5+3\sqrt{2}\right)\left( 5-3\sqrt{2}\right)}\\ =\frac{5-3\sqrt{2} +5+3\sqrt{2}}{25-18} =\frac{10}{7}\\ Bài\ 16:\\ a.\ \frac{\sqrt{2}\sqrt{7}}{7}\\ b.\ \frac{\sqrt{31x^{2}}}{31}\\ c.\frac{b\sqrt{5b}}{7\sqrt{a}} =\frac{b\sqrt{5ab}}{7a}\\ d.\ -7xy\frac{4}{\sqrt{xy}} =-28\sqrt{xy} \end{array}$