What are the single thread-like cells on the root epidermis called?

The single thread-like cells on the root epidermis are called root hairs.

Root hairs are slender extensions of individual epidermal cells, usually found in the zone of maturation near a root tip. They greatly increase the root’s surface area, allowing the plant to absorb more water and dissolved mineral nutrients from the soil. Although they look like tiny fibers, each root hair is a living extension of one cell rather than a separate multicellular organ.

Root hairs are easily confused with rootlets or trichomes. Rootlets are small branches of a root system, while trichomes are hair-like structures found on many plant surfaces, especially stems and leaves. Root hairs are specialized specifically for absorption and close contact with soil particles.

They are also important in plant–microbe relationships. In legumes, for example, root hairs can curl around nitrogen-fixing bacteria and help initiate the formation of root nodules. Older hairs are eventually shed as the root grows through the soil.