On the other hand, I think of $1/\sqrt3$ as 'simpler' in that it is just the reciprocal of root three, as opposed to being root three divided by three.

Certainly depends on the wider context, but I wonder if you really have easier time calculating or manipulating that, in general.

@tommy: That assumes that the numerical value is what you are interested in. Which is sometimes the case, but certainly not always.

@celtschk I know. I would personally leave it as $1/\sqrt 3$, but that comes with quite a lot of practice and abstraction. But I do think that the evaluation is a nice basic task that allows checking for cognitive load, and worth a try. I was surprised how big the difference turned out to be; I was about to write an answer that this is a stupid convention with no value, but it seems not so.

@tommi: One case where the $1/\sqrt{3}$ definitely is more useful is as coefficient in a quantum state: You see immediately that the absolute square (which gives the corresponding probability) is $1/3$, which for $\sqrt{3}/3$ takes more cognitive load to see. Therefore which convention is more useful definitely depends on what the expression is used for.

Perhaps ironically, for CPUs, computing $1/\sqrt x$ is often faster than computing $\sqrt x$. One way to see why this might be so is to compare the Newton-Raphson iterations. For $y=\sqrt x$, we get: $y_{n+1}=y_n/2+x/(2y_n)$. For $y=1/\sqrt x$, we get: $y_{n+1}=y_n(3-xy_n^2)/2$. The key difference here is that the latter does not require division by a varying quantity each iteration. Division is quite a lot more expensive than multiplication or addition for typical CPU number representations.

@Derek Elkins, I would say that the key difference is that division by 2 isn't really division in binary floating point representations: it's subtraction applied to the exponent. (I'm sure you know this already, but I didn't think it came through clearly in the explanation).