Question

Answer 1

\(A=\dfrac{\sqrt{3+\sqrt{5-\sqrt{13+4\sqrt{3}}}}}{\sqrt{6}+\sqrt{2}}=\dfrac{\sqrt{3+\sqrt{5-\left(2\sqrt{3}+1\right)}}}{\sqrt{6}+\sqrt{2}}\\ A=\dfrac{\sqrt{3+\sqrt{4-2\sqrt{3}}}}{\sqrt{2}\left(\sqrt{3}+1\right)}=\dfrac{\sqrt{3+\left(\sqrt{3}-1\right)}}{\sqrt{2}\left(\sqrt{3}+1\right)}\\ A=\dfrac{\sqrt{2+\sqrt{3}}}{\sqrt{2}\left(\sqrt{3}+1\right)}=\dfrac{\sqrt{4+2\sqrt{3}}}{2\left(\sqrt{3}+1\right)}=\dfrac{\sqrt{3}+1}{2\left(\sqrt{3}+1\right)}=\dfrac{1}{2}\)