No, you should not soak turmeric root before refrigerating it. Soaking can introduce moisture, which promotes mold growth and reduces its shelf life.
Turmeric root, like ginger, is best stored dry in the refrigerator. Moisture is the enemy when it comes to preserving fresh roots. When you soak turmeric root, you're essentially creating a breeding ground for bacteria and mold. Instead of soaking, simply brush off any excess dirt with a dry cloth or soft brush. If the turmeric is particularly dirty, you can quickly rinse it under cold water, but be sure to thoroughly dry it with a clean towel before storing. To further protect it, wrap the dried turmeric root in a paper towel and then place it in a resealable plastic bag or airtight container. This helps absorb any excess moisture and keeps the turmeric fresh for a longer period. Storing it in the crisper drawer of your refrigerator is also a good practice, as it provides a more stable temperature and humidity level.
If you find that your turmeric root is starting to soften or show signs of mold, you can still salvage some of it. Cut away any affected areas and use the remaining good portion immediately or freeze it for later use. Freezing turmeric root is a great way to preserve it for extended periods.