A student is asked to solve b^2+a^2=c^2 for a and gives the following
solution. Assume all variables represent positive Real Numbers. 

(Step 1)       
(Step 2)       
(Step 3)       b+a=c

That step is wrong. This mistake is trying to use a rule that applies 
only to MULTIPLIED quantities under a square root radical for ADDED 
quantities under a radical. If b2a2 had been under the radical and we had 
had  that would have given  but since b2 and a2 are added under 
the radical the rule doesn't work. So step (3) should be:



We cannot take ADDED squared terms from under a square root radical individually
like we can MULTIPLIED squared terms under a square root radical.  So we have
to leave the problem like that. 

Edwin