In the expression sqrt("cat"), what is the formal name of "cat"? This is more of a semantic question than an actual math question but I couldn't see where better to put it.
If I would write a silly equation like the aforementioned $ \sqrt{"cat"} $, what is the proper name for the "cat" portion?
Can one say it's not in the domain? Is it a type error? 
UPDATED
Perhaps I didn't explain it perfectly. Square Root, or Radical of "cat" makes no sense. I'm looking for the word that describes a data type that makes no sense in a mathematical context.
 A: +1 This is not a silly question, it a question that belongs to computer science or programming more than mathematics.
In mathematics one plays the role of compiler that is aware of the types that can be used, so there was no need to have a terminology for such instances.
However in programming, things like this are the bread and butter of programmers, specially in the strongly typed languages like Java,Delphi,C# etc. , but in languages like php one could very well get away with it until the expression needs to be evaluated (when program runs).
So borrowing from the cs/programming world words like : invalid argument (for the current context), unsupported argument (type) etc.
However if you have a way to define $cat^k$, then you can also formally define $\sqrt{cat}$ using formal Taylor power series. 
A: In the expression $\sqrt{x}$, $x$ is referred to as the radicand: http://mathworld.wolfram.com/Radicand.html
If you literally mean that you pass the string "$cat$" as an argument to the square root function (that is, if $f(x) = \sqrt{x}$ and you wish to compute $f(cat)$):  It doesn't make sense to pass a string value to a numeric function.  This is because strings are out of the domain of math...  (essentially)
A: This is a nice question. It, however, seems slightly philosophical.
If we look at $cat$ as being the multiplication of three variables $c,a,$ and $t$, then $\sqrt{cat}$ is defined in a mathematical context.
However, if we look at $c,a,$ and $t$ as letters which are not variables, $\sqrt{cat}$ has no mathematical meaning since $\sqrt{x}$ is a function from $\mathbb{R}$ to $\mathbb{R}$ or a relation from $\mathbb{R}$ to $\mathbb{C}$. In either case, $cat$ is not in $\mathbb{R}$. In fact, $cat$ does not even stand for a number.
I would think that the best way of expressing this is that $cat$ is "not in the domain".
A: We say that the argument is "ill-typed" or "improperly typed" or something of that sort meaning that it is the wrong type of argument. The opposite is "well-typed".
A: The question is asking what we call the number whose root we are getting. Similarly, with the expression $\frac{dog}{cow}$, dog is the numerator and cow is the denominator.
In the case of $\sqrt{cat}$, cat is called the "radicand".
