Radish would probably germinate within a week since you probably are not experiencing extremely cold weather.
Once they come up in a neat row (if you sowed the seeds that way) or scattered -- looking all the same -- you can take out any weeds that are not radish as well as thin the seedlings as they germinate. At the very least keep the leaves from overlapping.
Weeds that are too close may need to be cut rather than pulled so as not to disturb the desirable seedlings. Weeders/hoes with sharp cutting edge works well, but you can also use an old kitchen or steak knife as well.