If p is even then let p = 2q. p>=2 implies q>=1

Then sqrt(4*10^p) = 2*10^q. The two nearest squares to 4*10^p are 4*10^p + 1 +/- 2*10^q.

With q>=1, those nearest squares are too far from 4*10^p to be equal to 4*10^p+9, therefore if p is an even integer then 4*10^p+9 is never a perfect square.