That is definitely not true. If we had started with [tex] \sqrt{x} +\sqrt{y} [/tex] we could not add them. This is because not only do the indexes have to be the same (square root, cubed root, fourth root, etc), the radicands have to be the same as well. While the rules are not quite so restrictive with multiplying where you can in fact multiply those square roots together, it is breaking the rules to add them. If you can't add them to put them back together, then you can't take them apart like that in the first place.
