\(\left(\sqrt{8-\sqrt{15}}+\sqrt{8+\sqrt{15}}\right):\sqrt{5}\) \(=\dfrac{\sqrt{2}.\left(\sqrt{8-\sqrt{15}}+\sqrt{8+\sqrt{15}}\right)}{\sqrt{2}.\sqrt{5}}\)
\(=\dfrac{\sqrt{16-2\sqrt{15}}+\sqrt{16+2\sqrt{15}}}{\sqrt{2}.\sqrt{5}}\) \(=\dfrac{\sqrt{\left(\sqrt{15}-1\right)^2}+\sqrt{\left(\sqrt{15}+1\right)^2}}{\sqrt{2}.\sqrt{5}}\)
\(=\dfrac{\sqrt{15}-1+\sqrt{15}+1}{\sqrt{2}.\sqrt{5}}\)
\(=\dfrac{2\sqrt{15}}{\sqrt{2}.\sqrt{5}}=\dfrac{\sqrt{2}.\sqrt{2}.\sqrt{5}.\sqrt{3}}{\sqrt{2}.\sqrt{5}}=\dfrac{\sqrt{2}.\sqrt{3}}{1}=\sqrt{6}\)
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