SOLUTION: what can we multiply to rationalize the denominator? {{{ (sqrt( 2 )xy^2)/(cube root of( 8 )xy^3) }}}

The cube root of 8 is 2 so we can take the 8 out of
the root and put 2 in front of the radical on the bottom.

The cube root of y3 is y so we can take the 3 out of
the root and put y in front of the radical on the bottom



The y in the bottom cancels into the y in the top.



To clear the cube root in the bottom multiply top and bottom by 
.  That will make the bottom become 







Now the x's cancel:





You can either leave it like that or get all to one root:

 =  = 


 =  = 

Edwin