This recipe comes from Serious Eats. The same method can be used for turnips and carrots.
2 cups water
1 ½ tablespoons sea salt
3 bunches radishes, trimmed and cut into ½ to ¼” thick slices
1. Wash one wide mouth quart mason jar and a quarter pint jar.
2. Bring water and salt to boil in a small saucepan, stirring until salt dissolves. Let cool to room temperature.
3. Pack radish slices into the quart jar and cover with cooled brine, leaving about ½” headspace.
4. Fit the quarter pint jar into the mouth of the quart jar and pour the rest of the brine into it. Press the small jar down until brine reaches the brim of the big jar, so that the radishes are completely submerged.
5. Let radishes sit on your counter for 5-7 days until the brine goes slightly cloudy and the radishes taste tart and crunchy. When they’ve reached the level of tang that you like, remove the small jar, place a lid on the quart jar, and refrigerate.