[tex](3-2\sqrt 2)\cdot \sqrt{17+12\sqrt 2}+\sqrt{7+4\sqrt 3}\cdot \sqrt{3-2\sqrt 2} = \\ \\ = (3-2\sqrt 2)\cdot \sqrt{(\sqrt 8 +\sqrt 9)^2} +\sqrt{(\sqrt 3 +2)^2}\cdot \sqrt{(\sqrt 2 - 1)^2} = \\ \\ = (3-2\sqrt 2)\cdot |\sqrt 8+3| + |\sqrt 3+2|\cdot |\sqrt 2 - 1| = \\ \\ =(3-2\sqrt 2)\cdot (3+2\sqrt 2)+(\sqrt 3+2)(\sqrt 2-1) = \\ \\ = 9 - 8 + \sqrt 6 - \sqrt 3+2\sqrt 2 - 2 = \\ \\ = \sqrt 6 -\sqrt 3 +2\sqrt 2-1[/tex]
