Cockroaches are pretty easy to kill. The reason simply is that they use their front legs to eat.
That means that whatever they walk in they eat. Spiders, ants and so on do not, which makes them somewhat harder to kill.
So with cockroaches there are basically three options.
Firstly, there is surface spray. The good thing about this is that it is selective. That is, you only spray it where you want it to go. So, for example, you might spray it in warm moist areas, all around skirting boards and so on. The cockroaches walk in it, and as soon as they eat something they are dead.
A more recent approach is the fogger. This is an aerosol can with a nozzle that clicks into the on position, so it dispenses the entire contents of the can in one go. You use these by setting a few of them around the house before you leave.
It then creates a fog of insecticide, which settles into and onto everything. As part of this approach you will have removed all the cutlery and cooking implements from your kitchen, and then afterwards you wipe down the bench areas. So the insecticide is now on shelves, cupboard doors and the floor.
These work very well, although one or two places have blown themselves up by using too many of them, and filling the air with a flammable hydrocarbons propellant.
The third approach of course is baits. Baits are clean and simple – you just set them and forget them. The cockroaches are attracted by the food inside them, they eat it, and then go away to die.
Although they do work well, the drawback of baits is that they will not eliminate a population. They will control it to a low level but not eliminate it.
One further thing to add is that if you live in a block of units and other units in your block have cockroaches, then I’m afraid you never will eliminate them, because they will come through the roofing, air vents and plumbing.