Who are we? The problem is to create a leash of a certain length. If you can make a leash exactly one unit long, then you can also make a leash exactly √2 units long; the fact that the ratio of the two numbers is irrational doesn't impede this in any way.
No, the context is whatshisface claiming that there is a (resolvable) tension between the concept of an exact representation and an infinite decimal expansion, and gowld responding that decimal expansions are irrelevant. That doesn't support the idea that we're talking about digital representation; it undermines it.
But those are not symbols. We're talking symbols (digits).