Woo woo. Take it off baby! When you receive root veggies with the greens attached, it's important to remove the tops from the roots.
The greens are edible if they're in good shape--yes, even radish greens--and don't think that just because they are wilted that they are not good. They are just thirsty! Why? Because the roots and the greens are competing for the moisture in the plant. This is why you want to separate them. It will help keep your greens perky and your roots firm. Just cut off the roots below the rubber band or twist tie and store them in a plastic bag--feel free to spritz them or give them a dunk in water before you store them.
If any of the greens you get from us--whether cooking greens or salad greens--are a bit wilty, just soak them in water for a bit and they will revive. We just don't have the high tech set up of the misters that the grocery stores have.