$B= \dfrac{\sqrt{7-\sqrt{5}}+\sqrt{7+\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}.\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\=\dfrac{\sqrt{(\sqrt{7-\sqrt{5}}+\sqrt{7+\sqrt{5}})^2}}{\sqrt{7+2\sqrt{11}}}.\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{4}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\=\dfrac{\sqrt{7-\sqrt{5}+2\sqrt{(7-\sqrt{5})(7+\sqrt{5})+7+\sqrt{5}}}}{\sqrt{7+2\sqrt{11}}}.\dfrac{(\sqrt{2}+\sqrt{3}+\sqrt{4})+(\sqrt{4}+\sqrt{6}+\sqrt{8})}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\=\dfrac{\sqrt{14+4\sqrt{11}}}{\sqrt{7+2\sqrt{11}}}.\dfrac{(\sqrt{2}+\sqrt{3}+\sqrt{4})+\sqrt{2}(\sqrt{2}+\sqrt{3}+\sqrt{4})}{(\sqrt{2}+\sqrt{3}+\sqrt{4})}\\=\dfrac{\sqrt{2}(\sqrt{7+2\sqrt{11}})}{\sqrt{7+2\sqrt{11}}}.\dfrac{(\sqrt{2}+\sqrt{3}+\sqrt{4})(\sqrt{2}+1)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\=\sqrt{2}(\sqrt{2}+1)=2+\sqrt{2}$