\(\sqrt{11-6\sqrt{2}}-\sqrt{3-2\sqrt{2}}=\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{2}-1\right)^2}=3-\sqrt{2}-\left(\sqrt{2}-1\right)=4-2\sqrt{2}\)
\(\sqrt{41-12\sqrt{5}}-\sqrt{29-12\sqrt{5}}=\sqrt{\left(6-\sqrt{5}\right)^2}-\sqrt{\left(2\sqrt{5}-3\right)^2}=6-\sqrt{5}-2\sqrt{5}+3=9-3\sqrt{5}\)
\(\left(\sqrt{7}-\sqrt{3}\right)\sqrt{10+2\sqrt{21}}=\left(\sqrt{7}-\sqrt{3}\right)\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}=\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)=7-3=4\)
\(\left(\sqrt{6}-\sqrt{14}\right)\sqrt{5+\sqrt{21}}=\left(\sqrt{3}-\sqrt{7}\right)\sqrt{10+2\sqrt{21}}=-\left(\sqrt{7}-\sqrt{3}\right)\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}\)
\(=-\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)=-\left(7-3\right)=-4\)
\(\sqrt{9+\sqrt{17}}-\sqrt{9-\sqrt{17}}=\dfrac{\sqrt{18+2\sqrt{17}}-\sqrt{18-2\sqrt{17}}}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{17}+1\right)^2}-\sqrt{\left(\sqrt{17}-1\right)^2}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{17}+1-\sqrt{17}+1}{\sqrt{2}}=\dfrac{2}{\sqrt{2}}=\sqrt{2}\)
