$\sqrt{3 + 2\sqrt{2}} = \sqrt{1 + 2 + 2\sqrt{2}} = \sqrt{2 + 2\sqrt{2} + 1} = \sqrt{(\sqrt{2})^2 + 2 * 1 * \sqrt{2} + 1^2} = \sqrt{(\sqrt{2} + 1)^2} = |\sqrt{2} + 1| = \sqrt{2} + 1$

$\sqrt{7 + 4\sqrt{3}} = \sqrt{4 + 3 + 4\sqrt{3}} = \sqrt{4 + 4\sqrt{3} + 3} = \sqrt{2^2 + 2 * 2 * \sqrt{3} + (\sqrt{3})^2} = \sqrt{(2 + \sqrt{3})^2} = |2 + \sqrt{3}| = 2 + \sqrt{3}$

$\sqrt{11 + 2\sqrt{30}} = \sqrt{5 + 6 + 2\sqrt{30}} = \sqrt{5 + 2\sqrt{30} + 6} = \sqrt{(\sqrt{5})^2 + 2\sqrt{5 * 6} + (\sqrt{6})^2} = \sqrt{(\sqrt{5} + \sqrt{6})^2} = |\sqrt{5} + \sqrt{6}| = \sqrt{5} + \sqrt{6}$