0}|\cdot 2\cdot (3+2\sqrt2)=\\\\=2\cdot (3-2\sqrt2)\cdot (3+2\sqrt2)=2\cdot (9-4\cdot 2)=2" alt="24)\; \; \sqrt{17-12\sqrt{2}}\cdot (6+4\sqrt2)=\sqrt{17-2\cdot \sqrt{6^2\cdot 2}}\, \cdot (6+4\sqrt2)=\\\\= \sqrt{17-2\cdot \sqrt{8\cdot 9}} \cdot (6+4\sqrt2)= \sqrt{(\sqrt9-\sqrt8)^2} \cdot (6+4\sqrt2)=\\\\=\sqrt{(3-2\sqrt2)^2}\cdot (6+4\sqrt2)=|\underbrace {3-2\sqrt2}_{>0}|\cdot 2\cdot (3+2\sqrt2)=\\\\=2\cdot (3-2\sqrt2)\cdot (3+2\sqrt2)=2\cdot (9-4\cdot 2)=2" align="absmiddle" class="latex-formula">