First, we calculate that there are a total of $4 \cdot 4=16$ possibilities. Now, we list all of two-digit perfect squares. $64$ and $81$ are the only ones that can be made using the spinner. Consequently, there is a $\frac{2}{16}=$ (B) $\frac{1}{8}$ probability that the number formed by the two spinners is a perfect square. 
The arrows on the two spinners shown below are spun. Let the number $N$ equal $10$ times the number on Spinner $A$, added to the number on Spinner $B$. What is the probability that $N$ is a perfect square number? (2022 AMC 8 Problems, Question \#12) 
[A] $\frac{1}{16}$ 
[B] $\frac{1}{8}$ 
[C] $\frac{1}{4}$ 
[D] $\frac{3}{8}$ 
[E] $\frac{1}{2}$ 