Answer
Approximately 1.87 years. The value given in Appendix C is 1.88 years.
Work Step by Step
Let the distance between earth and sun's center be $R_{E}$.
Then, Mars-sun distance = 1.52$\times R_{E}$
Time period of earth = 1 year
We use Kepler's third law to obtain Time period of Mars in years.
If $T_{M}$ is the Time period of Mars, then
$\frac{(T_{M})^{2}}{1 year}$= $\frac{(1.52\times R_{E})^{3}}{(R_{E})^{3}}$
Or
$T_{M}= (1.52)^{3/2} \times 1 year$ = 1.87 years.
