Thoroughly rinse the beets and their leaves. Remove the leaves and store them for later use. Trim the ends from the beets and set aside.
Add all remaining ingredients to a small saucepan and bring to a boil. Meanwhile, tightly pack the trimmed radishes into a glass jar and set aside (depending on the size of the radishes, you may need to use two glass jars). Remove the saucepan from the heat and allow the brine to cool slightly, about one to two minutes. Pour the brine into the glass jar, being sure to cover the radishes completely. Allow the brine to cool to room temperature. Seal the jar with a tight fitting lid. When kept covered and chilled, the pickled radishes will keep well for 1-2 weeks.