$\begin{array}{l}A = (2 - \sqrt3)\sqrt{7 + 4\sqrt3} + (2\sqrt2 + 3)\sqrt{17} - 3\sqrt{32}\\ \to A = (2-\sqrt3)\sqrt{(2 + \sqrt3)^2} + (2\sqrt2 + 3)\sqrt{(3 - 2\sqrt2)^2}\\ \to A = (2 - \sqrt3)(2 + \sqrt3) + (2\sqrt2 + 3)(3 - 2\sqrt2)\\ \to A = (4 - 3) + (9 - 8) = 2\\ B = (\sqrt5 + 3)\sqrt{14 -6\sqrt5}- (3+2\sqrt5)\sqrt{29 - 12\sqrt5}\\ \to B = (\sqrt5 + 3)\sqrt{(3 - \sqrt5)^2} - (3 + 2\sqrt5)\sqrt{(2\sqrt5 - 3)^2}\\ \to B = (\sqrt5 + 3)(3 - \sqrt5) - (3 + 2\sqrt5)(2\sqrt5 - 3)\\ \to B = (9 - 5) - (20 - 9) = -7\\ C = \sqrt{4 - 2\sqrt3} + \sqrt{7 - \sqrt{48}}\\ \to C = \sqrt{(\sqrt3 - 1)^2} + \sqrt{(2 - \sqrt3)^2}\\ \to C = \sqrt3 - 1 + 2 - \sqrt3\\ \to C = 1\end{array}$
