To prove something is transcendental we would need to know how to compute it exactly, and I’m struggling to see how that would come up frequently in a physics c

To prove something is transcendental we would need to know how to compute it exactly, and I’m struggling to see how that would come up frequently in a physics context. In physics most constants are not arbitrary real numbers derived from a formula, they’re a measured relationship, which sort of inherently can’t be proved to be transcendental