Answer
$v = 0.707~c$
Work Step by Step
The relativistic momentum is $~~p = \gamma ~m~v = m~c$
Then:
$\gamma~v = c$
$\gamma = \frac{c}{v}$
We can find the speed when $\gamma = \frac{c}{v}$:
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
$\sqrt{1-\frac{v^2}{c^2}} = \frac{1}{\gamma}$
$1-\frac{v^2}{c^2} = \frac{1}{\gamma^2}$
$1-\frac{v^2}{c^2} = \frac{v^2}{c^2}$
$1 = \frac{2v^2}{c^2}$
$v^2 = \frac{1}{2}~c^2$
$v = \sqrt{\frac{1}{2}}~c$
$v = 0.707~c$
