There can be no solution to this problem because the 1/2 power
is the same as the square root and square roots can only be taken 
of non-negative numbers to give non-negative numbers.

This equation

(p/q)^(1/2) + (q/p)^(1/2) + (n/l)^(1/2) = 0

which is equivalent to

 +  +  = 0 

is three non-negative numbers adding up to 0.  This is impossible
unless they were all three 0.  But that is impossible because
if the first term were 0 then p would have to be 0.  But that would 
mean that the second term would have a zero in the denominator
which is undefined.  So this problem has no solution.  Sorry.  If
there is a typo, then you may give the correct problem in the thank-
you note.

Edwin