Concatenate number to get perfect square

If $N$ is a 1-digit number, the number $\overline{NN}$ cannot be a perfect square.

If $N$ is a 2-digit number, the number $\overline{NN}$ cannot be a perfect square.

Is the following statement True or False?

If $N$ is a $n$ -digit number with $n\ge 3$ , the number $\overline{NN}$ cannot be a perfect square?

Explanation: The number $\overline{NN}$ is made by concatenating the digits of $N$ and itself.

For example, if $N=2018$ then $\overline{NN}=20182018$ .