Answer
The proof is below.
Work Step by Step
We know that the gravitational potential energy is:
$\frac{GMm}{r}$.
We set this equal to kinetic energy, since the radius of the earth is essentially negligible compared to infinite distance:
$\frac{GMm}{r}=\frac{1}{2}mv^2$.
$v = \sqrt{\frac{2GM}{r}}$
This is more than the escape speed, which is $\sqrt{\frac{2GM}{r}}$.
