$\displaystyle \begin{array}{{>{\displaystyle}l}} a)\sqrt{9-\sqrt{17}} .\sqrt{9+\sqrt{17}}\\ =\sqrt{\left( 9-\sqrt{17}\right)\left( 9+\sqrt{17}\right)}\\ =\sqrt{81-17} =\sqrt{64} =8\\ b) \ 2\sqrt{2}\left(\sqrt{3} -2\right) +\left( 1+2\sqrt{2}\right)^{2} -2\sqrt{6}\\ =2\sqrt{6} -4\sqrt{2} +1+8+4\sqrt{2} -2\sqrt{6}\\ =9\\ \\ \end{array}$