I've found this amazing hydroponics book with information that I've been looking for for a long time. I'm going to post information on the ten root vegetables that are listed with instructions on how to grow them. This is the introduction to the chapter:
"Root vegetables and tubers, such as potato and sweet
potato, can also be grown in hydroponics. This important
part of the diet can be very productive in
deep media hydroponic growers.
Roots will need more space to grow under the surface
so media growers for roots are constructed at least 30
cm (12”) deep. The media should be deep enough to
keep the root area in a environment that is not saturated
with water, but still kept moist.
Root vegetables can be a part of everyday diet. A
soup can be made with soybeans and fresh vegetables
from the garden. A basic soup that includes a cup of
cooked soybeans should provide each family member
with about 400 calories, and about 1/2 of the protein
required for the day.
Potatoes were one of the first crops grown by Gericke,
the modern day father of hydroponics. He grew a fine
crop of potatoes under his tomato plants in a California
greenhouse. Potatoes are very high is carbohydrates
and provide daily energy.
Many root vegetables can also be kept through the
winter or slower growing season by harvesting and
storing or drying. They can also be kept alive in the
hydroponic beds if the temperatures can be kept
above freezing. Even in the northern temperate climates
the root vegetables can stay alive through the 8
hour sun days, although don’t expect much growth.
Many root vegetables take a longer to grow, sometimes
as much as 120 days to harvest. Many, such as
carrots, cannot be transplanted. This means that the
areas of the grower which are being harvested should
be replanted as soon as possible to keep a supply of
roots from the garden."
Quoted from "Home Hydroponic Gardens" by Peggy Bradley & Cesar Maruland