$\sqrt{10 + 8\sqrt{2 + \sqrt{9 + 4\sqrt{2}}}} = \sqrt{10 + 8\sqrt{2 + \sqrt{8 + 4\sqrt{2} + 1}}} = \sqrt{10 + 8\sqrt{2} + \sqrt{(2\sqrt{2} + 1)^2}} = \sqrt{10 + 8\sqrt{2 + 2\sqrt{2} + 1}} = \sqrt{10 + 8\sqrt{(\sqrt{2} + 1)^2}} = \sqrt{10 + 8(\sqrt{2} + 1)} = \sqrt{10 + 8\sqrt{2} + 8} = \sqrt{2(5 + 4\sqrt{2} + 4)} = \sqrt{2} * \sqrt{9 + 4\sqrt{2}} = \sqrt{2} * \sqrt{8 + 4\sqrt{2} + 1} = \sqrt{2} * \sqrt{(2\sqrt{2} + 1)^2} = \sqrt{2} * (2\sqrt{2} + 1) = 2\sqrt{4} + \sqrt{2} = 2 * 2 + \sqrt{2} = 4 + \sqrt{2}$

$\sqrt{22 + 6\sqrt{3 + \sqrt{13 + \sqrt{48}}}} = \sqrt{22 + 6\sqrt{3 + \sqrt{12 + \sqrt{16 * 3} + 1}}} = \sqrt{22 + 6\sqrt{3 + \sqrt{(2\sqrt{3} + 1)^2}}} = \sqrt{22 + 6\sqrt{3 + 2\sqrt{3} + 1}} = \sqrt{22 + 6\sqrt{(\sqrt{3} + 1)^2}} = \sqrt{22 + 6(\sqrt{3} + 1)} = \sqrt{22 + 6\sqrt{3} + 6} = \sqrt{28 + 6\sqrt{3}} = \sqrt{27 + 6\sqrt{3} + 1} = \sqrt{(3\sqrt{3} + 1)^2} = 3\sqrt{3} + 1$