Answer
$\gamma = 196.159$
Work Step by Step
We can express the energy in units of joules:
$(100.000\times 10^6~eV)(\frac{1.6\times 10^{-19}~J}{1~eV}) = 1.6\times 10^{-11}~J$
We can find $\gamma$:
$K = mc^2(\gamma-1)$
$\frac{K}{mc^2} = \gamma-1$
$\gamma = \frac{K}{mc^2}+1$
$\gamma = \frac{1.6\times 10^{-11}~J}{(9.109 381 88\times 10^{-31}~kg)(3.0\times 10^8~m/s)^2}+1$
$\gamma = 195.159+1$
$\gamma = 196.159$
