[tex]E = \sqrt{2-\sqrt{3}+\sqrt{5-\sqrt{13+\sqrt{48}}}}\\ \\\\ \sqrt{13+\sqrt{48}} = \sqrt{13+4\sqrt{3}} = \sqrt{(2\sqrt{3}+1)^2} = 2\sqrt{3}+1 \\ \sqrt{5-(2\sqrt{3}+1)} = \sqrt{4-2\sqrt{3}} = \sqrt{(\sqrt{3}-1)^2} = |\sqrt{3}-1| = \sqrt{3}-1\\ \\\\E = \sqrt{2-\sqrt{3}+(\sqrt{3}-1)} =\sqrt{2-\sqrt{3}+\sqrt{3}-1} = \sqrt{1}\\ \\\Rightarrow \boxed{E = 1 \in \mathbb{Q}}[/tex]
