Answer
$\beta = 0.999987$
Work Step by Step
In part (a), we found that $\gamma = 196.159$
We can find $\beta$:
$\gamma = \frac{1}{\sqrt{1-\beta^2}}$
$\sqrt{1-\beta^2} = \frac{1}{\gamma}$
$1-\beta^2 = \frac{1}{\gamma^2}$
$\beta^2 = 1-\frac{1}{\gamma^2}$
$\beta = \sqrt{1-\frac{1}{\gamma^2}}$
$\beta = \sqrt{1-\frac{1}{196.159^2}}$
$\beta = 0.999987$