[latex] \frac{ \sqrt{8} }{ \sqrt{64} - \sqrt[6]{8} } [/latex]

[latex] \frac{ \sqrt{8} }{ \sqrt{64} - \sqrt[6]{8} } [/latex] [latex]\frac{ \sqrt{8} }{ \sqrt{64} - \sqrt[6]{8} }= \frac{ \sqrt{2^2*2} }{ \sqrt{8^2} - \sqrt[2*3]{2^{1*3}} }= \frac{ 2\sqrt{2} }{ 8 - \sqrt[2]{2^{1}} }= \frac{ 2\sqrt{2} }{ 8 - \sqrt{2} }=\frac{ 2\sqrt{2}*(8 + \sqrt{2})}{ (8 - \sqrt{2})*(8 + \sqrt{2}) }=[/latex] [latex]=\frac{ 2\sqrt{2}*(8 + \sqrt{2})}{ 8^2 - (\sqrt{2})^2 }= \frac{ 2\sqrt{2}*(8 + \sqrt{2})}{ 64 - 2}= \frac{ 2*\sqrt{2}*(8 + \sqrt{2})}{ 2*31}=\frac{ \sqrt{2}*(8 + \sqrt{2})}{31}=[/latex] [latex]=\frac{ 8\sqrt{2}+2}{31}[/latex]