[StefanKarpinski]

I think you’ve hit the nail on the head:

> it could also be interpreted as ... [the] inverse of the square root (which is just the squaring operation)

Since the other obvious interpretation is not very useful and has a clearer name—i.e. “the square”—the term “inverse square root” has only one useful meaning, which is therefore how it’s interpreted. (I don’t follow the second option about binary operators.) Mathematical terminology and notation in general are full of ambiguities which are resolved by extensive contextual knowledge. As noted by a sibling comment, calling it the reciprocal square root would be clearer.