  In this short note we confirm the relation between the generalized
$abc$-conjecture and the $p$-rationality of number fields. Namely, we prove
that given K$/\mathbb{Q}$ a real quadratic extension or an imaginary
$S_3$-extension, if the generalized $abc$-conjecture holds in K, then there
exist at least $c\,\log X$ prime numbers $p \leq X$ for which K is
$p$-rational, here $c$ is some nonzero constant depending on K. The real
quadratic case was recently suggested by B\"ockle-Guiraud-Kalyanswamy-Khare.
