\(B=\frac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}=\frac{2\sqrt{3+\sqrt{5-\sqrt{12+2.\left(2\sqrt{3}\right).1+1}}}}{\sqrt{6}-\sqrt{2}}=\frac{2\sqrt{3+\sqrt{5-\left(2\sqrt{3}+1\right)}}}{\sqrt{6}-\sqrt{2}}\)
\(B=\frac{2\sqrt{3+\sqrt{4-2\sqrt{3}}}}{\sqrt{6}-\sqrt{2}}=\frac{2\sqrt{3+\sqrt{\left(1-\sqrt{3}\right)^2}}}{\sqrt{6}-\sqrt{2}}=\frac{2\sqrt{3+\sqrt{3}-1}}{\sqrt{6}-\sqrt{2}}=\frac{2\sqrt{2+\sqrt{3}}}{\sqrt{6}-\sqrt{2}}\)
\(B=\frac{\sqrt{2}\sqrt{4+2\sqrt{3}}}{\sqrt{6}-\sqrt{2}}=\frac{\sqrt{2}\sqrt{\left(1+\sqrt{3}\right)^2}}{\sqrt{2}\left(\sqrt{3}-1\right)}=\frac{\sqrt{2}.\left(\sqrt{3}+1\right)}{\sqrt{2}\left(\sqrt{3}-1\right)}=\frac{\sqrt{3}+1}{\sqrt{3}-1}=\frac{\left(\sqrt{3}+1\right)^2}{3-1}=\frac{4+2\sqrt{3}}{2}=2+\sqrt{3}\)
