$\begin{array}{l} a) \, 9 \,\,và\,\,6 + 2\sqrt2\\ Ta\,\,có:\\ +)\quad 9 = 6 + 3 = 6 + \sqrt9\\ +) \quad 6 + 2\sqrt2 = 6 + \sqrt8\\ Do\,\,\sqrt 8 < \sqrt9\\ nên\,\,6 + \sqrt8 < 6 + \sqrt9\\ hay \,\,6 + 2\sqrt2 < 9\\ b) \,\sqrt2 + \sqrt3 \,\,và\,\,3\\ Ta\,\,có:\\ +) \quad (\sqrt2 + \sqrt3)^2 = 5 + 2\sqrt6\\ +) \quad 3^2 = 9 = 5 + 4 = 5 + 2.2 = 5 + 2\sqrt4\\ Do\,\,\sqrt4 < \sqrt6\\ nên\,\,5 + 2\sqrt4 < 5 + 2\sqrt6\\ hay \,\,9 < (\sqrt2 + \sqrt3)^2\\ \Rightarrow 3 < \sqrt2 + \sqrt3\\ c)\,16\,\,và \,\,9+ 4\sqrt5\\ Ta \,\,có:\\ +)\quad 16 = 9 + 7 = 9 +\sqrt{49}\\ +) \quad 9 + 4\sqrt5 = 9 + \sqrt{80}\\ Do\,\,\sqrt{49} < \sqrt{80}\\ nên\,\,9 + \sqrt{49} < 9 + \sqrt{80}\\ hay\,\,16 < 9 + 4\sqrt5\\ d)\,\sqrt{11} - \sqrt3 \,\,và\,\,2\\ Ta\,\,có:\\ +)\quad (\sqrt{11} - \sqrt{3})^2 = 14 - 2\sqrt{33}\\ +) \quad 2^2 = 4 = 14 - 10 = 14 - 2.5 = 14 - 2\sqrt{25}\\ Do\,\,\sqrt{25} < \sqrt{33}\\ nên\,\,-\sqrt{25} > - \sqrt{33}\\ hay\,\,14 - 2\sqrt{25} > 14 - 2\sqrt{33}\\ \Rightarrow 2^2 > (\sqrt{11} - \sqrt3)^2\\ \Rightarrow 2 > \sqrt{11}- \sqrt3 \end{array}$
