$E=\sqrt{\dfrac{2}{8+\sqrt{15}}}+\sqrt{\dfrac{2}{8-\sqrt{15}}}\\↔\dfrac{1}{2}E=\sqrt{\dfrac 1 4}.\left(\sqrt{\dfrac{2}{8+\sqrt{15}}}+\sqrt{\dfrac{2}{8-\sqrt{15}}}\right)\\↔\dfrac{1}{2}E=\sqrt{\dfrac 1 4}.\sqrt{\dfrac{2}{8+\sqrt{15}}}+\sqrt{\dfrac 1 4}.\sqrt{\dfrac{2}{8-\sqrt{15}}}\\↔\dfrac{1}{2}E=\dfrac{1}{\sqrt{2(8+\sqrt{15})}}+\dfrac{1}{\sqrt{2(8-\sqrt{15})}}\\↔\dfrac{1}{2}E=\dfrac{1}{\sqrt{16+2\sqrt{15}}}+\dfrac{1}{\sqrt{16-2\sqrt{15}}}\\↔\dfrac{1}{2}E=\dfrac{1}{\sqrt{15+2\sqrt{15}+1}}+\dfrac{1}{\sqrt{16-2\sqrt+1}}\\↔\dfrac{1}{2}E=\dfrac{1}{\sqrt{(\sqrt{15}+1)^2}}+\dfrac{1}{\sqrt{(\sqrt{15}-1)^2}}\\↔\dfrac{1}{2}E=\dfrac{1}{|\sqrt{15}+1|}+\dfrac{1}{|\sqrt{15}-1|}\\↔\dfrac{1}{2}E=\dfrac{1}{\sqrt{15}+1}+\dfrac{1}{\sqrt{15}-1}\\↔\dfrac{1}{2}E=\dfrac{\sqrt{15}+1+\sqrt{15}-1}{(\sqrt{15}+1)(\sqrt{15}-1)}\\↔\dfrac{1}{2}E=\dfrac{2\sqrt{15}}{14}\\↔\dfrac{1}{2}E=\dfrac{\sqrt{15}}{7}\\↔E=\dfrac{2\sqrt{15}}{7}$
Vậy $E=\dfrac{2\sqrt{15}}{7}$
