$\begin{array}{l} 17)\,\sqrt{15 - \sqrt{3 -\sqrt{29 - 12\sqrt5}}}\\ = \sqrt{15 - \sqrt{3- \sqrt{20 - 2.3.2\sqrt5 + 9}}}\\ = \sqrt{15 - \sqrt{3 -\sqrt{(2\sqrt5 - 3)^2}}}\\ = \sqrt{15 - \sqrt{3 -2\sqrt5 + 3}}\\ =\sqrt{15 - \sqrt{5 -2\sqrt5 + 1}}\\ = \sqrt{15 - \sqrt{(\sqrt5 + 1)^2}}\\ = \sqrt{15 - \sqrt5 - 1}\\ = \sqrt{14 - \sqrt5}\\ 18) \, \sqrt{13 + 30\sqrt{2 + \sqrt{9 + 4\sqrt2}}}\\ = \sqrt{13 + 30\sqrt{2 + \sqrt{(2\sqrt2 + 1)^2}}}\\ = \sqrt{13 + 30\sqrt{2 + 2\sqrt2 + 1}}\\ =\sqrt{13 + 30\sqrt{(\sqrt2 + 1)^2}}\\ = \sqrt{13 + 30(\sqrt2 + 1)}\\ = \sqrt{25 + 2.5.3\sqrt2 + 18}\\ = \sqrt{(5 + 3\sqrt2)^2}\\ = 5 + 3\sqrt2\\ 19)\, (3 - \sqrt5)(\sqrt{10}-\sqrt2).\sqrt{3 + \sqrt5}\\ = \sqrt{3 -\sqrt5}.\sqrt2.(\sqrt5 -1).(\sqrt{3 - \sqrt5}.\sqrt{3 + \sqrt5})\\ = \sqrt{6 - 2\sqrt5}.(\sqrt5 - 1).2\\ = \sqrt{(\sqrt5 -1)^2}(\sqrt5 - 1).2\\ = (\sqrt5 - 1)^2.2\\ = (6 - 2\sqrt5).2\\ = 12 - 4\sqrt5\\ 20)\,(4 + \sqrt{15})(\sqrt{10} - \sqrt6).\sqrt{4 - \sqrt{15}}\\ = \sqrt{4 + \sqrt{15}}.\sqrt2.(\sqrt5 - \sqrt3).(\sqrt{4 + \sqrt{15}}.\sqrt{4 - \sqrt{15}})\\ = \sqrt{8 + 2\sqrt{15}}.(\sqrt5 - \sqrt3)\\ = \sqrt{(\sqrt5 + \sqrt3)^2}.(\sqrt5 - \sqrt3)\\ = (\sqrt5 + \sqrt3)(\sqrt5 - \sqrt3)\\ = 2 \end{array}$
