Question

$\frac{ \sqrt{8} }{ \sqrt{64} - \sqrt[6]{8} }$

Answer 1

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