You know those times when your doing maths and then for some reason you just CANNOT work out why a particular mathematical situation is that way! Well I just did.

FOr the life of me I cannot work out why the following happens:

How come

$\displaystyle \sqrt {x^2+y^2}\not= x + y $

Here is my thinking here.

$\displaystyle

\sqrt {x^2+y^2}

= \sqrt {x^2} + \sqrt {y^2}

= x + y

$

Please help me out. Because I just have no idea.