Question 49529
  
  3/{[(5)^(1/2)]+[(6)^(1/2)]}
 
  = {{{3/(sqrt(6)+sqrt(5))}}}  .... By multiplying both numerator & denominator by {{{(sqrt(6)-sqrt(5))}}}, we get
 
  = {{{(3(sqrt(6)-sqrt(5)))/(sqrt(6)+sqrt(5))(sqrt(6)-sqrt(5))}}} = {{{(3(sqrt(6)-sqrt(5)))/(6-5)}}} = {{{(3(sqrt(6)-sqrt(5)))/1}}}  Answer.  
 
  I hope this is clear to you.  In your question, the denominator, it is sqrt(5)+sqrt(6).  As both are positive, I took sqrt(6)+sqrt(5) as denominator so that the value of the expression will not change. If it is taken as it is as in the problem, then the answer will be in negative i.e. it will be {{{(-3(sqrt(6)-sqrt(5)))/(1)}}}

   
gsm