The answer to 'how to kill cockroach' is to use a combination of targeted insecticides, baits, and traps. Start by thoroughly cleaning your home to remove food sources and hiding places for cockroaches. Then, apply insecticides in areas where you've seen cockroach activity, such as under sinks, behind appliances, and along baseboards. Place baits and traps in strategic locations to attract and kill cockroaches. Repeat this process every few months to maintain control.
If the cockroach problem persists or you're uncomfortable using chemicals, it's best to call a professional pest control technician. They have access to more powerful treatments and can develop a customized plan to eliminate the infestation.