We can rewrite this expression as:

#sqrt(32)/sqrt(8) => sqrt(8 * 4)/sqrt(8)#

Now, we can use this rule for radicals to rewrite the numerator and complete the simplification:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#sqrt(color(red)(8) * color(blue)(4))/sqrt(8) =>#

#(sqrt(color(red)(8)) * sqrt(color(blue)(4)))/sqrt(8) =>#

#(cancel(sqrt(color(red)(8))) * sqrt(color(blue)(4)))/color(red)(cancel(color(black)(sqrt(8)))) =>#

#sqrt(color(blue)(4)) =>#

#2#

We can also use this rule of radicals to rewrite and simplify the expression:

#sqrt(color(red)(a))/sqrt(color(blue)(b)) = sqrt(color(red)(a)/color(blue)(b))#

#sqrt(color(red)(32))/sqrt(color(blue)(8)) =>#

#sqrt(color(red)(32)/color(blue)(8)) =>#

#sqrt(4) =>#

#2#