Warts do not have roots.
More Info: Warts that have little black dots in the center are often referred to as “seed” warts. Many believe that this darkened center is the root of the wart. It is not a root, but the dried blood of a dead capillary.
What Causes Warts?
Common skin warts are caused by one of 23 of the more than 100 subtypes of the human papillomavirus (HPV).  As a virus, it is contagious and is spread from coming in contact with the virus. It can be contracted directly, from person to person, or indirectly, from object to person.
Healthy Skin Protects from Warts
One of the major functions of the skin, the largest organ of the human body, is protection. The epidermis, the surface layer of the skin, is made up of epithelial cells that act as a barrier to protect the underlying tissue against temperature, impacts, radiation, chemicals, and microorganisms, such as the HPV virus.  Healthy skin does not allow the virus to enter the body. In fact, in studies, the HPV virus is commonly found on healthy skin that is free of warts. 
HPV Waits for Its Opportunity
The HPV virus becomes a problem when the skin becomes lacerated. Once the body’s protective layer is compromised, it rushes in to invade the epithelial cells. Once it infects the cells, they begin to quickly multiply.
How Warts Develop
When the skin receives a skin laceration, the epithelial cells work to resurface the wound, known as epitheliaslisation. 
When HPV infects the epithelial cells, they begin to multiply uncontrollably producing a skin mass that grows to protrude beyond the skin’s surface called a wart. 
What Are Those “Black Dots”
In some cases, a wart may have a little black dot in the center, often referred to as “seed” warts. Some assume that this little black dot is the root of the wart. This “root” is actually the end of a capillary that has grown up into the wart as it was developing. Each layer of skin produced by the epithelial cells covers the tip of the capillary until it is ultimately smothered and dies. The little black dot is the dried blood of the tip of a capillary. 
  de Koning, MN. “High Prevalence of Cutaneous Warts in Elementary School Children and the Ubiquitous Presence of Wart-associated Human Papillomavirus on Clinically Normal Skin.” The British Journal of Dermatology 172.1 (2015): 196-201. Print.
 “Epithelial Tissues.” Epithelial Tissue. Web. 1 Feb. 2015. The Department of Biodiversity and Conservation Biology, The University of Western Cape. http://www.botany.uwc.ac.za/sci_ed/grade10/mammal/Epithelial.htm
 “Phases of Wound Healing.” Phases of Wound Healing. Web. 1 Feb. 2015. <http://www.clinimed.co.uk/wound-care/education/wound-essentials/phases-of-wound-healing.aspx>.
 “Nongenital Warts .” Nongenital Warts. Web. 1 Feb. 2015. <http://emedicine.medscape.com/article/1133317-overview>.
 “Phases of Wound Healing.” Warts: IU Health Center. Web. 1 Feb. 2015. <http://healthcenter.indiana.edu/answers/warts.shtml>.