Using a sharp knife, trim the peel from the grapefruits, removing as much of the white pith as possible. Working over a large, shallow bowl in order to catch the juices, segment the grapefruit into slices, cleanly separating the flesh from the membrane. (For a helpful how-to video, watch here.) Let the slices fall into the bowl, then squeeze any remaining juice from the fruit into the bowl before discarding the scraps.
Add the beets, radishes, and olive oil to the bowl and toss until well combined. Season with salt and pepper.