ROOT

in botany, that part of a plant normally underground. Its primary functions are anchorage of the plant, absorption of water and dissolved minerals and conduction of these to the stem, and storage of reserve foods. Many plants develop subterranean structures that are in reality specialized stems (e.g., corms, tubers). The root differs from these mainly by lacking leaf scars and buds, having a root cap, and having branches that originate from internal tissue rather than from buds. The primary root, or radicle, is the first organ to appear when a seed germinates. It grows downward into the soil, anchoring the seedling. In gymnosperms and dicotyledons, the radicle becomes a taproot. It grows downward, and branch, or secondary, roots grow laterally from it. This type of system is called a taproot system. In some plants, such as carrots and turnips, the taproot serves as a storage organ and becomes swollen with foodstuffs. Grasses and other monocotyledons have a fibrous root system, characterized by a mass of roots of about equal diameter. This network of roots does not arise as branches of the primary root but consists of many branching roots that emerge from the base of the stem. Roots grow in length only from their ends. The very tip of the root is covered by a protective, thimble-shaped root cap. Just behind the root cap lies the apical meristem, a tissue of actively dividing cells. Some of the cells produced by the apical meristem are added to the root cap, but most of them are added to the region of elongation, which lies just above the meristematic region. It is in the region of elongation that growth in length occurs. Above this elongation zone lies the region of maturation, where the primary tissues of the root mature, completing the process of cell differentiation that actually begins in the upper portion of the meristematic region. The primary tissues of the root are, from outermost to innermost, the epidermis, the cortex, and the vascular cylinder. The epidermis is composed of thin-walled cells and is usually only one cell layer thick. The absorption of water and dissolved minerals occurs through the epidermis, a process greatly enhanced in most land plants by the presence of root hairsslender, tubular extensions of the epidermal cell wall that are found only in the region of maturation. The absorption of water is chiefly via osmosis, which occurs because (1) water is present in higher concentrations in the soil than within the epidermal cells (where it contains salts, sugars, and other dissolved organic products) and (2) the membrane of the epidermal cells is permeable to water but not to many of the substances dissolved in the internal fluid. These conditions create an osmotic gradient, whereby water flows into the epidermal cells. This flow exerts a force, called root pressure, that helps drive the water through the roots. Root pressure is partially responsible for the rise of water in plants, but it cannot alone account for the transport of water to the top of tall trees. The cortex conducts water and dissolved minerals across the root from the epidermis to the vascular cylinder, whence it is transported to the rest of the plant. The cortex also stores food transported downward from the leaves through the vascular tissues. The innermost layer of the cortex usually consists of a tightly packed layer of cells, called the endodermis, which regulates the flow of materials between the cortex and the vascular tissues. The vascular cylinder is interior to the endodermis and is surrounded by the pericycle, a layer of cells that gives rise to branch roots. The conductive tissues of the vascular cylinder are usually arranged in a star-shaped pattern. The xylem tissue, which carries water and dissolved minerals, comprises the core of the star; the phloem tissue, which carries food, is located in small groups between the points of the star. The older roots of woody plants form secondary tissues, which lead to an increase in girth. These secondary tissues are produced by the vascular cambium and the cork cambium. The former arises from meristematic cells that lie between the primary xylem and phloem. As it develops, the vascular cambium forms a ring around the primary vascular cylinder. Cell divisions in the vascular cambium produce secondary xylem (wood) to the inside of the ring and secondary phloem to the outside. The growth of these secondary vascular tissues pushes the pericycle outward and splits the cortex and epidermis. The pericycle becomes the cork cambium, producing cork cells (outer bark) that replace the cortex and epidermis. Some roots, called adventitious roots, arise from an organ other than the rootusually a stem, sometimes a leaf. They are especially numerous on underground stems. The formation of adventitious roots makes it possible to vegetatively propagate many plants from stem or leaf cuttings. Roots are not always underground. When they arise from the stem and either pass for some distance through the air before reaching the soil or remain hanging in the air, they are called aerial. They are seen well in corn (maize), screw pine, and banyan, where they eventually assist in supporting the plant. in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula. Ninth-century Arab writers called one of the equal factors of a number a root, and their medieval translators used the Latin word radix (root, adjective radical). If a is a positive real number and n a positive integer, there exists a unique positive real number x such that xn = a. This numberthe (principal) nth root of ais written n. The integer n is called the index of the root. For n = 2, the root is called the square root and is written . The root 3 is called the cube root of a. If a is negative and n is odd, the unique negative nth root of a is termed principal. If a whole number (specific integer) has a rational nth rooti.e., one that can be written as a common fractionthen this root must be an integer. Thus 5 has no rational square root since 22 is less than 5 while 32 is greater than 5. Exactly n complex numbers satisfy the equation xn = 1, and they are called the complex nth roots of unity. If a regular polygon of n sides is inscribed in a unit circle centred at the origin so that one vertex lies on the positive half of the x-axis, the radii to the vertices are the vectors representing the n complex nth roots of unity. If the root the vector of which makes the smallest positive angle with the positive direction of the x-axis is denoted by the Greek letter omega, w, then w, w2, w3, . . . , wn = 1 constitute all of the nth roots of unity. Thus w = -1/2 + 1/2, w2 = -1/2 - 1/2, w3 = 1 are the cube roots of unity. Any root, symbolized by the Greek letter epsilon, e, that has the property that e, e2, . . . , en = 1 give all of the nth roots of unity is called primitive. Evidently the problem of finding the nth roots of unity is equivalent to the problem of inscribing a regular polygon of n sides in a circle. For every integer n, the nth roots of unity can be determined in terms of the rational numbers by means of rational operations and radicals; but they can be constructed by ruler and compasses (i.e., determined in terms of the rational operations and square roots) only if n is a product of distinct prime numbers of the form 2h + 1, or 2k times such a product, or is of the form 2k. If a is a complex number not 0, the equation xn = a has exactly n roots. All of the nth roots of a are the products of any one of these roots by the nth roots of unity. The term root has been carried over from the equation xn = a to all polynomial equations. Thus a solution of the equation f(x) = a0xn + a1xn - 1 + . . . + an - 1x + an = 0, a0 0 is called a root of the equation. If the coefficients lie in the complex field, an equation of the nth degree has exactly n not necessarily distinct complex roots. If the coefficients are real and n is odd, there is a real root. But an equation does not always have a root in its coefficient field. Thus x2 - 5 = 0 has no rational root.