The palmetto bugs which are also known as the American Cockroach can lay up to 14 eggs each week.
During a lifetime the Palmetto bugs or cockroaches can lay up to 90 eggs in a lifetime and each one of those eggs can hatch one baby palmetto bug or cockroach per egg.
Cockroaches can multiply pretty quickly and once a cockroach lays an egg the egg will hatch the young within a month.
So you need to get rid of the eggs and the cockroaches as well.
I would highly recommend hiring an exterminator to get rid of the roaches when you see them to prevent an infestation.
Once you get an infestation of cockroaches it becomes really hard to get rid of them.