Then what exactly do you mean by “exterminate them”.
If you’re talking about the extremists only, how would that be done? Also, even if it were done, there are more extremists waiting in the wings, and more after that. Muslims have one of the highest birthrates in the world. And many of them groom their young to become extremists and terrorists. It’s a high calling.
You will never “exterminate” them because the next wave is always coming of age.
The best option we have is to contain them in their own lands where they can be as extremist as they want among other Muslims. That has been the way of centuries, except when Spain had to push them out of the continent ... but they should never have let them in in the first place. Nor should we or any country that cares about peace and stability.
Let them stay in their own countries and lands. They will then have to deal with their own problems of overpopulation, underdevelopment and resource scarcity.
How do you accomplish that when their goal is to infiltrate out land to kill us? Do you wait for them to find a way to get a nuke to go off within our borders, or do you take action to ensure they can't make that happen?