I'm not questioning the pedagogy in the original comment, just the specific math. x^(1/10) takes a value of dimension [length^10] to a value of dimension [length].
Interestingly, I think you could take this in a few aesthetic directions. From a pure math perspective, this is where you can start talking about set theory, cardinality, etc. Irrational numbers are infinite sequences of digits we can only approximate. From a computer science perspective, you can talk about Newton's method, and also make the argument than an algorithm which converges to a number is a quite meaningful way to describe that number. Some would also add a caveat of 'efficiently' converging. And combining the two perspectives together, you can discuss that the set of computable numbers are of a lower cardinality than the set of reals -- aka 0% of real numbers are computable. You could also look at things from a geometrical perspective, and show how roots higher than square roots are tied to higher dimensions are are nonconstructible in the plane (this might be very hard to show!).