Originally Posted by

**topsquark** OUCH!!! I think this is either a trick problem or that your friend needs to pay more attention to the details. Look at the RHS for the last two lines. For arbitrary a and b (such that a, b, and a - b are positive):

$\displaystyle \sqrt{a} - \sqrt{b} \neq \sqrt{a - b}$

Just pick a couple of a and b values to prove it to yourself. So either the problem was designed to give a correct result despite the error in the Mathematics, or your friend was very lucky indeed to get the correct answer using this method.

-Dan