The answer is $\boxed{6}$.

A square number can only end with $0$, $1$, $4$, $5$, $6$, and $9$. Hence, the candidate of last two digits are $70$, $71$, $74$, $75$, $76$, and $79$.

Meanwhile, a square number must satisfy $n^2\equiv 0, 1\pmod{4}$. Among these candidates, only $76$ meets this criteria. Therefore, we conclude that the answer is $6$.