What is the distance between the foci of the hyperbola $x^2 - 4y^2 = 1$?

The given equation of the hyperbola is $x^2 - 4y^2 = 1$.

This can be rewritten in the standard form as $\dfrac{x^2}{1} - \dfrac{y^2}{1/4} = 1$.

Comparing with $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$, we get $a^2 = 1$ and $b^2 = \dfrac{1}{4}$.

The eccentricity $e$ of the hyperbola is given by $e = \sqrt{1 + \dfrac{b^2}{a^2}}$.

$e = \sqrt{1 + \dfrac{1/4}{1}} = \sqrt{\dfrac{5}{4}} = \dfrac{\sqrt{5}}{2}$

The distance between the foci of the hyperbola is $2ae$.

$2ae = 2 \times 1 \times \dfrac{\sqrt{5}}{2} = \sqrt{5}$

Answer: $\sqrt{5}$