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root,in mathematics, number or quantity r for which an equation f(r)=0 holds true, where f is some functionfunction,
in mathematics, a relation f that assigns to each member x of some set X a corresponding member y of some set Y; y is said to be a function of x, usually denoted f(x) (read "f of x ").
..... Click the link for more information. . If f is a polynomialpolynomial,
mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a1x
..... Click the link for more information. , r is called a root of f; for example, r=3 and r=−4 are roots of the equation x2+x−12=0, because (3)2+(3)−12=0 and (−4)2+(−4)−12=0. In the special case where f(x)=xn−a for some number a, a root of f is called an nth root of a, denoted by n√a or a1/n. For example, 2 is the third, or cube, root of 8 (∛8=2), since it satisfies the equation x3−8=0. Every number has n different (real or complex) nth roots; e.g., there are two square roots of 9 (3 and −3) since (3)(3)=9 and (−3)(−3)=9.
root,in botany, the descending axis of a plant, as contrasted with the stem, the ascending axis. In most plants the root is underground, but in epiphytesepiphyte
or air plant,
any plant that does not normally root in the soil but grows upon another living plant while remaining independent of it except for support (thus differing from a parasite).
..... Click the link for more information. the roots grow in the air and in hydrophytes (e.g., cattails and water lilies) they grow in water or marshes. Roots function to absorb water and dissolved minerals from the soil, to anchor the plant, and often to store food. There are two main types of root system: the tap-root system, in which there is a main primary root larger than the other branching roots; and the diffuse (or fibrous) root system, in which there are many slender roots with numerous smaller root branches. Tap roots are characteristic of most trees and of many other plants, including the carrot, parsnip, radish, beet, and dandelion. The grasses (e.g., corn, rye, and alfalfa) have diffuse roots; in the sweet potato some of the larger fibrous roots swell to store food—although these should not be confused with the tuber of the Irish potato, which is a modified underground stemstem,
supporting structure of a plant, serving also to conduct and to store food materials. The stems of herbaceous and of woody plants differ: those of herbaceous plants are usually green and pliant and are covered by a thin epidermis instead of by the bark of woody plants.
..... Click the link for more information. . Root systems often far exceed in mass the aboveground portions of the plant: alfalfa roots sometimes reach 40 ft (12 m) in length, and the combined length of all the roots of a mature rye plant has been measured at 380 mi (612 km). These ramified root systems are important agents in preventing soil erosion. Roots grow primarily in length; only the older roots may develop a cambium layer that increases their diameter. Protecting the constantly growing tip of the root is a cap of cells that break off as the root probes through the soil; they are replaced by new cells from a layer of meristematic tissue just behind them. In the center of the root the cells formed earlier by the embryonic cells of this layer differentiate into storage tissue and xylem and phloem vessels to conduct sapsap,
fluid in plants consisting of water and dissolved substances. Cell sap refers to this fluid present in the large vacuole, or cell cavity, that occupies most of the central portion of mature plant cells.
..... Click the link for more information. upward to the leaves and back down to nourish the root cells. On the surface of the epidermis of the growing portion of the root, tiny cellular projections called root hairs extend into the soil to absorb water and minerals. Although root hairs are less than 1-3 in. (.84 cm) long, their great number enables the plant to collect enormous quantities of water, most of which is promptly lost into the air by transpiration. In spite of their slenderness and delicate structure, the spiraling forward thrust of the root tips and the pressure of their expanding cells is sufficient to split solid rock.
The absorbing and anchoring organ of vascular plants. Roots are simple axial organs that produce lateral roots, and sometimes buds, but bear neither leaves nor flowers. Elongation occurs in the root tip. The older portion of the root, behind the root tip, may thicken through cambial activity. Some roots, grass for example, scarcely thicken, but tree roots can become 4 in. (10 cm) or more in diameter near the stem. Roots may be very long. The longest maple (Acer) roots are usually as long as the tree is tall, but the majority of roots are only a few inches long. The longest roots may live for many years, while small roots may live for only a few weeks or months.
Root tips and the root hairs on their surface take up water and minerals from the soil. They also synthesize amino acids and growth regulators (gibberellins and cytokinins). These materials move up through the woody, basal portion of the root to the stem. The thickened, basal portion of the root anchors the plant in the soil. Thickened roots, such as carrots, can store food that is later used in stem growth. See Cytokinin, Gibberellin
Roots usually grow in soil where: it is not too dense to stop root tip elongation; there is enough water and oxygen for root growth; and temperatures are high enough (above 39°F or 4°C) to permit root growth, but not so high that the roots are killed (above 104°F or 40°C). In temperate zones most roots are in the uppermost 4 in. (10 cm) of the soil; root numbers decrease so rapidly with increasing depth that few roots are found more than 6 ft (2 m) below the surface. Roots grow deeper in areas where the soil is hot and dry; roots from desert shrubs have been found in mines more than 230 ft (70 m) below the surface. In swamps with high water tables the lack of oxygen restricts roots to the uppermost soil layers. Roots may also grow in the air. Poison ivy vines form many small aerial roots that anchor them to bark or other surfaces.
The primary root originates in the seed as part of the embryo, normally being the first organ to grow. It grows downward into the soil and produces lateral second-order roots that emerge at right angles behind the root tip. Sometimes it persists and thickens to form a taproot. The second-order laterals produce third-order laterals and so on until there are millions of roots in a mature tree root system. In contrast to the primary root, most lateral roots grow horizontally or even upward. In many plants a few horizontal lateral roots thicken more than the primary, so no taproot is present in the mature root system.
Adventitious roots originate from stems or leaves rather than the embryo or other roots. They may form at the base of cut stems, as seen in the horticultural practice of rooting cuttings.
(radix), one of the principal vegetative organs in cormo-phytes (with the exception of mosses), which serves for the attachment of the plant to the substrate, the absorption of water and nutrients from the substrate, the primary conversion of a number of absorbed substances, the synthesis of organic compounds and their subsequent transport to the other plant organs, and the elimination of certain metabolic products. In some plants, the roots have additional functions, such as to serve as a receptacle for reserve materials. In soboliferous plants the roots serve as an organ of vegetative reproduction.
The root is an axial organ of the plant, related in origin to the stem; when the ancestors of terrestrial plants emerged on dry land they developed rhizomelike branches, the prototypes of roots, at the lower end of the sporophyte. Morphologically, the root differs from the stem in the absence of leaves, in the presence of the root cap, and in endogenous branching (the development of lateral roots in the interior parts of the root, or the pericycle).
The typical root is narrow-cylindrical or filamentous. The rudiment of the root already exists in the seed embryo, and when the seed sprouts, it develops into the main root. Acropetalous branching is characteristic (the younger lateral roots and their rudiments arising closer to the crown of the root). Many plants have adventitious roots in addition to the main and lateral roots. Externally, these do not differ from the lateral roots, and they perform the same functions. However, they usually develop on other organs of the plant—the stems, leaves, modified underground and aboveground shoots (bulbs, tubers, rhizomes)—and on older roots. The formation of adventitious roots is the factor that makes for the possibility of vegetative reproduction.
The tip of the root is covered by the root cap, which protects the tip against injury. The root grows in length by means of division of the cells of the apical meristem, in what is called the division zone, and because of significant lengthwise growth in the growth, or expansion, zone (usually 1–2 mm, sometimes to 10 mm). Behind the growth zone is the zone of absorption and differentiation, the outermost layer of which is differentiated into epiblem. The cells of the epiblem form the root hairs, which increase the absorption surface of the root from five to 20 times.
Differentiation of the meristem into the primary permanent tissues begins in the growth zone, but it is manifested distinctly in the absorption zone and in what is called the passage zone. The primary anatomic structure of the roots is similar in all seed plants. Underneath the layer of cells of the epiblem is the mul-tilayered primary cortex, which consists of thin-walled living parenchymal cells. In some plants the walls of the first to third outer layers of cells of the cortex, the exoderm, undergo suberi-zation; upon the atrophy of the epiblem, they assume a protective function. The innermost layer of the primary cortex, or the endoderm, consists of a single layer of cells whose walls are partially suberized or lignified (often thickened); only a few of these cells are unaltered.
Endoderm surrounds the central cylinder, or stele, of the root. One or more of the outer layers of its cells form the pericycle, whose thin-walled, living cells retain their meristematic activity over a long period. The lateral roots and the adventitious buds take form within the pericycle, and the secondary thickening of the root is accomplished with its participation. A large part of the central cylinder is taken up by the complex conducting radial fascicle, in which elements of the xylem and phloem alternate.
In monocotyledonous plants the primary anatomical structure of the root is retained throughout the plant’s life; in dicotyledonous and gymnospermous plants, it is replaced by a secondary structure. In the latter instance, the fascicular cambium deposits (between the xylem and phloem) secondary xylem, or wood, toward the center and secondary phloem, or bast, toward the periphery. The parenchyma of the primary medullary (bast and wood) ray is formed from the interfascicular cambium, located opposite the rays of primary xylem in the pericycle. The cork cambium, or phellogen, deposits cork cells toward the exterior, which becomes the covering tissue of the secondarily thickened root; the entire primary cortex is discarded. These changes cause increases in thickness in the root. A distinction is noted between growth roots, which grow quickly (under favorable circumstances, an average of 1–3 cm per day), thicken, undergo suberi-zation early, constitute the skeleton of the root system, and, in a number of instances, provide for the vegetative propagation of the plant; and suckers, which are thin, delicate, short, slow-growing, and usually short-lived.
All of the roots of a single plant considered together are known as the root system, whose general form and character are determined by the correlation of growth of the main, lateral, and adventitious roots. When the predominant growth is of the main root, a tap-root system is formed (lupine, cotton). When the main root is characterized by weak growth or early atrophy and the predominant development is of a large number of adventitious roots, a fibrous system is formed (monocotyledons; among dicotyledons, species of Ranunculus and Plantago).
The roots of cereal grasses (rye and wheat) penetrate to depths of 1.0-1.5 m; in alfalfa, to 10 m; and in woody plants, to 10–12 m, although hard ground usually impedes penetration deeper than 3–5 m. The area occupied by the root system of a single cereal plant may attain a diameter of 40–60 cm; of melon, 6–8 m; and of woody plants, 10–18 m, exceeding the diameter of the crown by several times. The total length of the roots of annuals may reach several km. The total root surface, including that of the root hairs, exceeds the surface of the aboveground organs by many times.
A distinction is made, according to distribution in the soil (depending on environment), between specialized (superficial or deep) root systems and universal root systems, which develop equally in width and in depth. For example, in the northern forest zone on podzolic soils, which are often oversaturated with moisture, poorly aerated, and have poorly penetrable subsoil, the root systems of plants are 90–95 percent concentrated at the surface layers of the soil (10–15 cm). In semidesert and desert zones, some plants have only surface roots, which take advantage of the precipitation of early spring (ephemera); others use the rains and the condensed moisture that precipitates at the upper layers of the soil at night (cacti); in still others, the roots reach ground waters (camel thorn).
Universal root systems make use of moisture at various levels of the water table at different times; as a result, the plants can grow all summer (Calligonum, Haloxylon, Ephedra). In zones of insufficient moisture there is marked stratification in the root distribution for the various species of plants growing in the same area. The ratio between the roots and the aboveground parts of the plants also depends on the soil and climatic conditions. In the wet northern zone, the mass of the root system is from five to ten times smaller than the mass of the aboveground parts of the plant.
The roots absorb the ions of mineral salts from the soil primarily, but also certain products of the life activities of soil microorganisms and the root excretions of other plants. The compounds of nitrogen, phosphorus, and sulfur absorbed by the roots interact with the products of photosynthesis that flow in from the leaves to form amino acids, nucleotides, and other organic compounds. Elements, in the form of ions (potassium, calcium, magnesium, phosphorus) or organic molecules (nitrogen, sulfur), pass into the leaves and stems along the veins of the xylem as a result of the action of root pressure and transpiration. Alkaloids, such as nicotine, growth hormones (kinins, gibberel-lins), and other physiologically active substances are also synthesized in the roots. In some plants (predominantly of the legume family), bacteria that induce the production of nodules from the root parenchyma inhabit the roots.
The roots discharge into the soil the ions of mineral salts, amino acids, sugar, urea, and phenolic compounds. In some plants, such as those of the nightshade family (Solanaceae) the roots also secrete auxins and substances of the gibberellin family, which stimulate plant growth; in others, they secrete gelatinous substances that form root-protective sheaths. Root secretions foster the development of soil microorganisms in the rhizo-sphere. As the plant grows, the amount of secretion decreases, and with it, the number of rhizosphere microorganisms. The nodular bacteria play an important role in the nitrogen nutrition of the plants and in increasing soil fertility. Mycorrhizae-form-ing fungi inhabit the surface or the interior of the roots of many woody and herbaceous plants, in which root hairs do not develop.
Adventitious buds that yield aerial shoots (in soboliferous plants) form on the roots of many plants. In a number of plants the roots serve as a repository for reserve nutrients (root crops). In certain tropical trees, the lateral or adventitious roots (slablike, stiltlike, or columnar), which serve for support and nutrition, branch off near the base of the trunk or from the limbs. Creeping lianas, such as ivy, develop holdfast roots. In the tropics, many epiphytes form adventitious aerial roots that absorb water from atmospheric precipitation through the multilayered surface of their tissue, called the velamen. In some tropical epiphytic orchids and in plants of the family Podostemaceae, the leaves and stems are underdeveloped; their vegetative organs are represented chiefly by flat green roots that perform the functions of assimilation. Plants living in oxygen-poor soils, such as the marsh cypress and the mangrove, have respiratory roots, or pneumatophores, whose crowns are located above the soil or water and supply the underground organs with air. In some palms and in plants of the family Rubiaceae, some of the horizontal roots are transformed into protective thorns. The roots of plants that parasitize trees, such as the mistletoe, have the appearance of long cylindrical rods distributed in the bark of the tree. In parasitic plants (broom rape, dodder) and semiparasites (cow wheat, yellow rattle), the root system develops poorly; at the same time, the endings of some of the roots embed themselves within the body of the host plant in the form of special suckers, or haustoria, which draw the nutrients from the host. In other plants, such as the hornwort and the bladderwort, roots are absent; this is due to special features of their life conditions.
The roots of many plants are widely used by man and have great nutritional and economic significance. Roots that contain starch, sugar, oils, alkaloids, latex, dyes, and other valuable substances are used in medicine and industry. Plants with highly developed root systems are used for holding shifting sands and eroded soils and for attachment to cliffs.
REFERENCESKrasovskaia, I. V. “Obzor rabot po morfologii i fiziologii kornei.” Trudy po prikladnoi botanike, genetike i selektsii, 1928, vol. 18, issue 5.
Krasovskaia, I. V. “Zakonomernosti stroeniia kornevoi sistemy khlebnykh zlakov.” Botanicheskii zhurnal, 1950, vol. 35, no. 4.
Shalyt, M. S. “Podzemnaia chast’ nekotorykh lugovykh, stepnykh i pustynnykh rastenii i fitotsenozov.” Trudy Botanicheskogo instituta AN SSSR, series 3. Geobotanika, 1950, issue 6.
Sabinin, D. A. Fiziologicheskie osnovy pitaniia rastenii. Moscow, 1955.
Kachinskii, N. A. Pochva, ee svoistva i zhizn’. Moscow, 1956.
Kolesnikov, V. A. Kornevaia sistema plodovykh i iagodnykh rastenii i metody ee izucheniia. Moscow, 1962.
Fedorov, A. A., M. E. Kirpichnikov, and Z. T. Artiushenko. Atlas po opisatel’noi morfologii vysshikh rastenii, vol. 2. Moscow-Leningrad, 1962.
Kolosov, 1.1. Poglotitel’naia deiatel’nost ‘kornevykh sistem rastenii. Moscow, 1962.
Rakhteenko, I. N. Rost i vzaimodeistvie kornevykh sistem drevesnykh rastenii. Minsk, 1963.
Voronin, N. S. “Evoliutsiia pervichnykh struktur ν korniakh rastenii.”
Uch. zap. Kaluzhskogo pedagogicheskogo instituta, 1964, issue 13.
Boiko, L. A. Fiziologiia kornevoi sistemy rastenii ν usloviiakh zasoleniia. Leningrad, 1969.
Esau, K. Anatomiia rastenii. Moscow, 1969. (Translated from English.)
O. N. CHISTIAKOVA, R. P. BARYKINA, and D. B. VAKHMISTROV
(in linguistics), a morpheme (morph) that is the common element of a group of words derived from it and having a basically common lexical meaning.
Roots are determined by eliminating all inflectional and derivational affixes—for example, Russian luch in the words luch, “ray”; luchi, “rays”; luchevoi, “ray” (adjective); and izluchenie, “radiation.” In some languages the root may undergo sound changes, as in the German find/fand/fund in the words finden, fand, gefunden, “to find,” and the Arabic h-s-b in the words hisā b, “account,” hāsib, “meter,” and muhtasib, “controller of weights and measures.” Compound words may contain two or more roots, as in the Russian luchevidnyi, “raylike” (roots luch + vid).
The etymological root is the form and meaning of a word, conceived as the original—for example, the Russian kol with the meaning of “circle” in the words koleso, “wheel,” and okolo, “around.”
(mathematics). (1) The nth root of a number a is a number x (denoted by whose nth power is equal to a (that is, xn = a). The operation of finding the root is called extraction of a root. When a ≠ 0, there are n different values (generally complex numbers) of the root; for example, the values of are 2, –1 + i, and –1 –i .
Many geometric problems posed by ancient mathematicians reduced to finding roots of numbers. Among Babylonian cuneiform writings (second millennium B.C.) there are descriptions of methods of approximating square roots, as well as tables of square roots. A special symbol is encountered in Egyptian papyri for the extraction of roots. Ancient Greek mathematicians established that the side of a square is not commensurable with its diagonal (equal to a if a is the length of a side), which later led to the discovery of irrational numbers. Aryabhata (fifth century) gave a rule for extracting square and cube roots. Omar Khayyam (second half of the 11th century or beginning of the 12th century), al-Kashi (15th century), and the German mathematician M. Stifel (16th century) extracted higher roots on the basis of the formula for (a + b)n. L. Euler (18th century) gave approximation methods for extracting roots that have retained their significance. Square roots of negative numbers, encountered in works by J. Cardan and R. Bombelli in the 16th century, led to the discovery of complex numbers.
(2) The root of the algebraic equation
(1) a0xn + a1xn-1 + . . . + an-1x + an = 0
is a number c that, when substituted for x, reduces the equation to an identity. The root of equation (1) is also called the root of the polynomial
f(x) = a0xn + a1xn-1 + . . . + an
If c is the root of the polynomial f(x), then f(x) is divisible without a remainder by x — c.
See root mode, go root, wheel.
root(1) (verb) To have access to all of the device's resources. See rooting.
(2) (noun) The highest privilege level the user has for accessing resources in the computer. See root level.
(3) The starting point in a structure. See root directory.