Simplify. Assume all variables represents positive 
numbers:
 ____
Öx4y3

Prime factor everything under the radical:
 _______
Öxxxxyyy

Since the index of the radical is understood to be 2,
group into twos, or pairs of like factors:
 _____________
Ö(xx)(xx)(yy)y

Now each pair of like factors can be written as a
square:
 _______
Öx2x2y2y

Take each square out in front as the base without the
exponent, leaving the y that did not pair under the
radical:
    _
xxyÖy

or
    _
x2yÖy

Edwin