It is possible to write \frac 2 4 or \frac \pi 4 to get 2/4 and \pi/4, respectively.

However, it is not possible to write \frac \sqrt{2} 2 to get \sqrt{2}/2.

Are there consistent rules on how to write shorthand \frac?

• Note that this is nothing to do with \frac per se: you will see the same with almost any commands where you provide single tokens as mandatory arguments. Aug 8, 2012 at 18:45
• Enclose the \sqrt{2} with {} to make it a single token. Aug 8, 2012 at 18:45

The command \frac has two mandatory arguments. So you can they the first two tokens are the arguments (or simple the first two groups).
\frac \sqrt{2} 2 fails because \sqrt is the first token, {2} the second one.