Colonizing the Moons

Logistics aside, would it really be possible to colonize the moons of the gas giants?

It's my understanding that planets tend to have radiation belts around them.  Would the massive radiation from a planet like Jupiter make it impossible to live on its moons or are some of them outside this belt?  Or could people just live in protected domes of some sort?

>>1
As far as I know, the radiation belts are much closer to the planets than the moons; for example Earth's Van Allen radiation belt ends at about 65,000 km, whereas Earth's moon sits at about 380,000 km. Moons close enough to be affected by a planet's radiation belt would likely experience tremendous tidal forces, making them unuseable for colonization.

Also, you can't make radiation protective domes. The dome would have to be made of solid lead or some other heavy metal to block the radiation; not only is this impractical for obvious reasons, but it would also block sunlight, making the inside of the dome uninhabitable.

I'm very curious about other factors affecting the colonization of moons. This is a fantastic question for /sci/; finally some intelligent scientific discussion.