  We argue that in the Generalized Uncertainty Principle (GUP) model, the
parameter $\beta_0$ whose square root, multiplied by Planck length $\ell_p$,
approximates the minimum measurable distance, varies with energy scales. Since
minimal measurable length and extra dimensions are both suggested by quantum
gravity theories, we investigate models based on GUP and one extra dimension,
compactified with radius $\rho$. We obtain an inspiring relation
$\sqrt{\beta_0} \ell_p/\rho \sim {\cal O}(1)$. This relation is also consistent
with predictions at Planck scale and usual quantum mechanics scale. We also
make estimations on the application range of the GUP model. It turns out that
the minimum measurable length is exactly the compactification radius of the
extra dimension.
