Question 964233
<pre>
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)       {{{ b^2+a^2=c^2 }}}
(Step 2)       {{{ sqrt( b^2+a^2 ) = sqrt( c^2 ) }}}
(Step 3)       b+a=c
<font color="indigo"><b>
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 b<sup>2</sup>a<sup>2</sup> had been under the radical and we had 
had {{{sqrt(b^2a^2)}}} that would have given {{{b*a}}} but since b<sup>2</sup> and a<sup>2</sup> are added under 
the radical the rule doesn't work. So step (3) should be:

{{{sqrt( b^2+a^2 ) = c }}}

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</pre>