Preheat oven to 400 degrees F. Move the rack to the middle position.
Remove the greens from the beets and the radishes and scrub them clean.
Quarter the beets, cutting them into equal size pieces. Add them to a mixing bowl with the olive oil, salt and pepper. Mix until fully coated.
Transfer the beets to a baking sheet and bake them for 20 minutes.
While the beets are baking, prepare the radishes. Add them to the mixing bowl with olive oil, salt and pepper. Mix to fully coat.
After the beets have roasted for 20 minutes, add the radishes to the baking sheet. Bake for another 15 minutes, or until the radishes are thoroughly roasted.
While the roots are a roasting, make the yogurt sauce.
Add the Greek yogurt, minced garlic, and chopped dill to a measuring cup and whisk to combine. Salt and pepper to taste. It is easy to over salt yogurt add so keep that in mind.
Remove the beets and radishes from the oven and plate them on a serving tray. Drizzle the yogurt sauce over them. Then top them off with fresh sprigs of dill and cracked black pepper.