Imagine you have never seen a root sign, , in your life.Consider the problem: . This means that for some reason you want the denominator to have only integer exponents. So . If we start with , then and even if we get the problem, , then .
What if we were using roots? The above problems would be transformed as follows. . This means that for some reason you want the denominator to have no roots. So . If we start with , then and even if we get the problem, , then
Which of the two techniques would be easier to explain? Or to teach? I think the first one. This is one of the reasons I think that radical parts of an algebra curriculum can be dispensed with. By the way the root method may not look to bad but that is only because I presented it second and your brain was already primed to see the pattern.