Answer
See answers.
Work Step by Step
The momentum is given by equation 26–4.
$$p=\gamma mv = \frac{\gamma mc^2 v}{c^2}$$
The energy is given by equation 26–6b, $E=\gamma mc^2$. Make a substitution.
$$p= \frac{E v}{c^2}$$
This can be solved for v.
$$v=\frac{pc^2}{E}$$
This was the first part of the relation to be proven. Now combine this with equation 26–9.
$$v=\frac{pc^2}{E}=\frac{pc^2}{\sqrt{p^2c^2+m^2c^4}}=\frac{pc}{\sqrt{p^2+m^2c^2}}$$
This is the relationship shown in the problem, which is now proven.