Here, b is a positive integer and a = 3.
$\therefore b=3 q+r$, for $0 \leq r<3$
This must be in the form $3 q, 3 q+1$ or $3 q+2$.
Now,
$(3 q)^{2}=9 q^{2}=3 m$, where $m=3 q^{2}$
$(3 q+1)^{2}=9 q^{2}+6 q+1=3\left(3 q^{2}+2 q\right)+1=3 m+1$, where $m=3 q^{2}+2 q$
$(3 q+2)^{2}=9 q^{2}+12 q+4=3\left(3 q^{2}+4 q+1\right)+1=3 m+1$, where $m=3 q^{2}+4 q+1$
Therefore, the square of a positive integer cannot be of the form 3m+2, where m is a natural number.