Answer
Please see the work below.
Work Step by Step
We know that
$\frac{T_{mars}^2}{T_{earth}^2}=(\frac{r_{mars}}{r_{earth}})^3$
This can be rearranged as:
$T_{mars}=\sqrt{(\frac{r_{mars}}{r_{earth}})^3}T_{earth}$
$T_{mars}=\sqrt{(1.52)^3}T_{earth}$
$T_{mars}=(1.874 years)(365.25)=680days$
