I have the following problem which i have no idea how to proceed.

Let G be a finite group with odd number of elements. Show that for every $\displaystyle g \in G$, there exists an element $\displaystyle h \in G$ such that $\displaystyle g=h^2$.

I have tried to construct a subgroup H of G defined by $\displaystyle H=\{h\in G \mid g=h^2, \forall g \in G \}. $ However, I cant proceed on after that. Perhaps someone can guide me on how to proceed on with this problem. Thank You.