Root hair

Root hairs, or absorbent hairs, are tubular outgrowths of a trichoblast, a hair-forming cell on the epidermis of a plant root. These structures are lateral extensions of a single cell and are only rarely branched. They are found in the region of maturation, also called the zone of differentiation of the root. Just prior to and during root hair cell development, there is elevated phosphorylase activity. Plants absorb water through the roots from the soil by bulk flow. Root hair cells are adapted to this process by increasing root surface area for the purpose of taking in more water. The large vacuole inside root hair cells makes this intake much more efficient.
Function.
Most water absorption happens in the root hairs. The root hairs are long which allows them to penetrate between soil particles, and prevent harmful bacterial organisms from entering the plant through the xylem vessels. Increasing the surface area of these hairs allows plants to be more efficient in absorbing nutrients and establish relationships with microbes.
Cross-section of root hair cell: a roughly rectangular shape with a long, thin tail extending to the right and a nucleus at the top left. This happens because the water in the soil has a higher water potential than the cytoplasm of the root hairs. The function of root hairs is to collect water and mineral nutrients that are present in the soil and take this solution up through the roots to the rest of the plant. As root hair cells do not carry out photosynthesis, they do not contain chloroplasts.
Formation.
Root hair cells are outgrowths at a tip of the plant's roots. Root hair cells vary between 15 and 17 micrometers in diameter, and 80 to 1,500 micrometers in length. They are found only in the zone of maturation, and not the zone of elongation, possibly because any root hairs that arise are sheared off as the root elongates and moves through the soil. 
Root hairs grow quickly, at least 1μm/min, making them particularly useful for research on cell expansion.
Fungi Interaction.
The function of root hairs are essential for healthy plant nutrition, but there are factors in the environment that can bring a positive change to them. Enhancements to root hair function that could be obtained for the plant highly depends on their interactions with the surrounding fungi. Symbiotic fungi are known to produce mycorrhizal symbioses like arbuscular mycorrhiza and ectomycorrhiza with the root hairs they interact with. These types of mycorrhizae seems to be the most common relationship, for which can be classified as occurring in 90% of terrestrial plant species, because of the benefits it brings to both the fungus and plant. The fungal species that seem to interact with root hairs the most in nature however, are the EM fungi that produce the ectomycorrhiza.
Formation of this symbiotic relationship first begins with the colonization of the root hairs by the EM fungi. This process begins when the EM fungus adheres to the root hair from the soil. The fungus then secretes diffusible factors that the root hairs are highly sensitive to which allow the hyphae to penetrate into the epidermal cells and in the first layers of the root cortex to create a Hairtig net. This highly branched structure serves as an interface between the two cooperating organisms as fungal cells adapt to the exchanges that will soon occur between the plant and newly attached fungus.
Importance.
Root hairs form an important surface as they are needed to absorb most of the water and nutrients needed for the plant. They are also directly involved in the formation of root nodules in legume plants. The root hairs curl around the bacteria which allows for the formation of an infection thread through into the dividing cortical cells to form the nodule.
Having a large surface area, the active uptake of water and minerals through root hairs is highly efficient. 
Root hair cells also secrete acid (H+ from malic acid) which exchanges and helps solubilize the minerals into ionic form, making the ions easier to absorb.
Survival.
This way, the root hair coverage stays the same. When a new root hair cell grows, it excretes a hormone so that the other cells in close proximity to it are unable to grow one of these hairs. This ensures equal and efficient distribution of the actual hairs on these cells. 
The act of re-potting or transplanting a plant can result in root hair cells being pulled off, perhaps to a significant extent, and such plants may therefore wilt for some time as a result.