In mathematics, the nth root of a number x is a number r which, when raised to the power of n, equals x

Failed to parse (Missing texvc executable; please see math/README to configure.): r^n = x,

where n is the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred to using ordinal numbers, as in fourth root, twentieth root, etc.

For example:

• 2 is a square root of 4, since 2² = 4.
• −2 is also a square root of 4, since (−2)² = 4.

A real number or complex number has n roots of degree n. While the roots of 0 are not distinct (all equaling 0), the n nth roots of any other real or complex number are all distinct. If n is even and the number is real and positive, one of its nth roots is positive, one is negative, and the rest are complex but not real; if n is even and the number is real and negative, none of the nth roots are real. If n is odd and the number is real, one nth root is real and has the same sign as the number, while the other roots are not real.

Roots are usually written using the radical symbol Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{\,\,}

or Failed to parse (Missing texvc executable; please see math/README to configure.): \surd{}

, with Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{x}\!\,

or Failed to parse (Missing texvc executable; please see math/README to configure.): \surd x
denoting the square root, Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[3]{x}\!\,
denoting the cube root, Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[4]{x}
denoting the fourth root, and so on. In the expression Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{x}

, n is called the index, Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{\,\,}

is the radical sign, and x is called the radicand. When a number is presented under the radical symbol, it must return only one result like a function, so a non-negative real root, called the principal nth root, is preferred rather than others. An unresolved root, especially one using the radical symbol, is often referred to as a surd[1] or a radical.[2] Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called a radical expression.

In calculus, roots are treated as special cases of exponentiation, where the exponent is a fraction:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{x} \,=\, x^{1/n}

Roots are particularly important in the theory of infinite series; the root test determines the radius of convergence of a power series. Nth roots can also be defined for complex numbers, and the complex roots of 1 (the roots of unity) play an important role in higher mathematics. Galois theory can be used to determine which algebraic numbers can be expressed using roots, and to prove the Abel-Ruffini theorem, which states that a general polynomial equation of degree five or higher cannot be solved using roots alone; this result is also known as "the insolubility of the quintic".

History[link]

The origin of the root symbol √ is largely speculative. Some sources imply that the symbol was first used by Arabic mathematicians. One of those mathematicians was Abū al-Hasan ibn Alī al-Qalasādī (1421–1486). Legend has it that it was taken from the Arabic letter ج, which is the first letter in the word Jadhir "root" in Arabic. (The dh in Jadhir is a voiced interdental fricative, like the th in English the.) Many scholars, however, including Leonhard Euler ^[3] believe it originates from the letter r, the first letter of radix "root" in Latin word referring to the same mathematical operation. The symbol was first seen in print without the vinculum (the horizontal "bar" over the numbers inside the radical symbol) in the year 1525 in Die Coss by Christoff Rudolff, a German mathematician.

The term surd traces back to al-Khwārizmī (c. 825), who referred to rational and irrational numbers as audible and inaudible, respectively. This later led to the Arabic asamm (deaf, dumb) for irrational number being translated as surdus (deaf or mute) into Latin. Gherardo of Cremona (c. 1150), Fibonacci (1202) and then Robert Recorde (1551) all used the term to refer to unresolved irrational roots.^[4]

Definition and notation[link]

The four 4th roots of −1,
none of which is real

The three 3rd roots of −1,
one of which is a negative real

The nth root of a number x, where n is a positive integer, is a number r whose nth power is x:

Failed to parse (Missing texvc executable; please see math/README to configure.): r^n = x.\!\,

Every positive real number x has a single positive nth root, which is written Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{x} . For n equal to 2 this is called the square root and the n is omitted. The nth root can also be represented using exponentiation as x^1/n.

For even values of n, positive numbers also have a negative nth root, while negative numbers do not have a real nth root. For odd values of n, every negative number x has a real negative nth root. For example, −2 has a real 5th root, Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[5]{-2} \,= -1.148698354\ldots

but −2 does not have any real 6th roots.

Every non-zero number x, real or complex, has n different complex number nth roots including any positive or negative roots, see complex roots below. The nth root of 0 is 0.

For most numbers, an nth root is irrational. For example,

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{2} = 1.414213562\ldots

All nth roots of integers, or in fact of any algebraic number, are algebraic.

For the extension of powers and roots to indices that are not positive integers, see exponentiation.

The character codes for the radical symbols are

Square roots[link]

The square root of a number x is that number r which, when squared, becomes x:

Failed to parse (Missing texvc executable; please see math/README to configure.): r^2 = x.\!\,

Every positive real number has two square roots, one positive and one negative. For example, the two square roots of 25 are 5 and −5. The positive square root is also known as the principal square root, and is denoted with a radical sign:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{25} = 5.\!\,

Since the square of every real number is a positive real number, negative numbers do not have real square roots. However, every negative number has two imaginary square roots. For example, the square roots of −25 are 5i and −5i, where i represents a square root of −1.

Cube roots[link]

A cube root of a number x is a number r whose cube is x:

Failed to parse (Missing texvc executable; please see math/README to configure.): r^3 = x.\!\,

Every real number x has exactly one real cube root, written Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[3]{x} . For example,

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[3]{8}\,=\,2\quad\text{and}\quad\sqrt[3]{-8}\,= -2.

Every real number has two additional complex cube roots (see complex roots below).

Identities and properties[link]

Every positive real number has a positive nth root and the rules for operations with such surds are straightforward:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b} \,,

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}} \,.

Using the exponent form as in Failed to parse (Missing texvc executable; please see math/README to configure.): x^{1/n}

normally makes it easier to cancel out powers and roots.

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{a^m} = \left(a^m\right)^{\frac{1}{n}} = a^{\frac{m}{n}}.

Problems can occur when taking the nth roots of negative or complex numbers. For instance:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{-1}\times\sqrt{-1} = -1

whereas

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{-1 \times -1} = 1

when taking the principal value of the roots. See failure of power and logarithm identities in the exponentiation article for more details.

Simplified form of a radical expression[link]

A radical expression is said to be in simplified form if^[5]

1. There is no factor of the radicand that can be written as a power greater than or equal to the index.
2. There are no fractions under the radical sign.
3. There are no radicals in the denominator.

For example, to write the radical expression Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{\tfrac{32}{5}}

in simplified form, we can proceed as follows. First, look for a perfect square under the square root sign and remove it: 

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{\tfrac{32}{5}} = \sqrt{\tfrac{16 \cdot 2}{5}} = 4 \sqrt{\tfrac{2}{5}}

Next, there is a fraction under the radical sign, which we change as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): 4 \sqrt{\tfrac{2}{5}} = \frac{4 \sqrt{2}}{\sqrt{5}}

Finally, we remove the radical from the denominator as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{4 \sqrt{2}}{\sqrt{5}} = \frac{4 \sqrt{2}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{4 \sqrt{10}}{5}

When there is a denominator involving surds it may be possible to find a factor to multiply both numerator and denominator by to simplify the expression. For instance using the factorization of the sum of two cubes:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{\sqrt[3]{a}+\sqrt[3]{b}} = \frac{\sqrt[3]{a^2}-\sqrt[3]{ab}+\sqrt[3]{b^2}}{(\sqrt[3]{a}+\sqrt[3]{b})(\sqrt[3]{a^2}-\sqrt[3]{ab}+\sqrt[3]{b^2})} = \frac{\sqrt[3]{a^2}-\sqrt[3]{ab}+\sqrt[3]{b^2}}{a+b} \,.

Simplifying radical expressions involving nested radicals can be quite difficult. It is not immediately obvious for instance that:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{3+2\sqrt{2}} = 1+\sqrt{2}\,

Infinite series[link]

The radical or root may be represented by the infinite series:

Failed to parse (Missing texvc executable; please see math/README to configure.): (1+x)^{s/t} = \sum_{n=0}^\infty \frac{\prod_{k=0}^{n-1} (s-kt)}{n!t^n}x^n

with Failed to parse (Missing texvc executable; please see math/README to configure.): |x|<1 . This expression can be derived from the binomial series.

Computing principal roots[link]

The nth root of an integer is not always an integer, and if it is not an integer then it is not a rational number. For instance, the fifth root of 34 is

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[5]{34} = 2.024397458 \ldots,

where the dots signify that the decimal expression does not end after any finite number of digits. Since in this example the digits after the decimal never enter a repeating pattern, the number is irrational.

The nth root of a number A can be computed by the nth root algorithm, a special case of Newton's method. Start with an initial guess x₀ and then iterate using the recurrence relation

Failed to parse (Missing texvc executable; please see math/README to configure.): x_{k+1} = \frac{1}{n} \left({(n-1)x_k +\frac{A}{x_k^{n-1}}}\right)

until the desired precision is reached.

Depending on the application, it may be enough to use only the first Newton approximant:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{x^n+y} \approx x + \frac{y}{n x^{n-1}}.

For example, to find the fifth root of 34, note that 2⁵ = 32 and thus take x = 32 and y = 2 in the above formula. This yields

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[5]{34} = \sqrt[5]{32 + 2} \approx 2 + \frac{2}{5 \cdot 16} = 2.025.

The error in the approximation is only about 0.03 %.

Newton's method can be extended to produce a generalized continued fraction for the nth root which can be modified in various ways as described in that article. For example:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{z^m} = \sqrt[n]{(x^n+y)^m} = x^m+\cfrac{my} {nx^{n-m}+\cfrac{(n-m)y} {2x^m+\cfrac{(n+m)y} {3nx^{n-m}+\cfrac{(2n-m)y} {2x^m+\cfrac{(2n+m)y} {5nx^{n-m}+\cfrac{(3n-m)y} {2x^m+\ddots}}}}}};

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{z^m}=x^m+\cfrac{2x^m\cdot my}{n(2z - y)-my-\cfrac{(1^2n^2-m^2)y^2}{3n(2z - y)-\cfrac{(2^2n^2-m^2)y^2}{5n(2z - y)-\cfrac{(3^2n^2-m^2)y^2}{7n(2z - y)-\ddots}}}}.

In the case of the fifth root of 34 above (after dividing out selected common factors):

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[5]{34} = 2+\cfrac{1} {40+\cfrac{4} {4+\cfrac{6} {120+\cfrac{9} {4+\cfrac{11} {200+\cfrac{14} {4+\ddots}}}}}} =2+\cfrac{4\cdot 1}{165-1-\cfrac{4\cdot 6}{495-\cfrac{9\cdot 11}{825-\cfrac{14\cdot 16}{1155-\ddots}}}}.

Complex roots[link]

Every complex number other than 0 has n different nth roots.

Square roots[link]

The square roots of i

The two square roots of a complex number are always negatives of each other. For example, the square roots of −4 are 2i and −2i, and the square roots of i are

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1 + i}{\sqrt{2}}\quad\text{and}\quad\frac{-1 - i}{\sqrt{2}}.

If we express a complex number in polar form, then the square root can be obtained by taking the square root of the radius and halving the angle:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{re^{i\theta}} \,=\, \pm\sqrt{r}\,e^{i\theta/2}.

A principal root of a complex number may be chosen in various ways, for example

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{re^{i\theta}} \,=\, \sqrt{r}\,e^{i\theta/2}

which introduces a branch cut in the complex plane along the positive real axis with the condition 0 ≤ θ < 2π, or along the negative real axis with −π < θ ≤ π.

Using the first(last) branch cut the principal square root Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt z

maps Failed to parse (Missing texvc executable; please see math/README to configure.): z
to the half plane with non-negative imaginary(real) part. The last branch cut is presupposed in mathematical software like Matlab or Scilab.

Roots of unity[link]

The three 3rd roots of 1

The number 1 has n different nth roots in the complex plane, namely

Failed to parse (Missing texvc executable; please see math/README to configure.): 1,\;\omega,\;\omega^2,\;\ldots,\;\omega^{n-1},

where

Failed to parse (Missing texvc executable; please see math/README to configure.): \omega \,=\, e^{2\pi i/n} \,=\, \cos\left(\frac{2\pi}{n}\right) + i\sin\left(\frac{2\pi}{n}\right)

These roots are evenly spaced around the unit circle in the complex plane, at angles which are multiples of Failed to parse (Missing texvc executable; please see math/README to configure.): 2\pi/n . For example, the square roots of unity are 1 and −1, and the fourth roots of unity are 1, Failed to parse (Missing texvc executable; please see math/README to configure.): i , −1, and Failed to parse (Missing texvc executable; please see math/README to configure.): -i .

[edit] nth roots

Every complex number has n different nth roots in the complex plane. These are

Failed to parse (Missing texvc executable; please see math/README to configure.): \eta,\;\eta\omega,\;\eta\omega^2,\;\ldots,\;\eta\omega^{n-1},

where η is a single nth root, and 1, ω, ω², ... ωⁿ⁻¹ are the nth roots of unity. For example, the four different fourth roots of 2 are

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[4]{2},\quad i\sqrt[4]{2},\quad -\sqrt[4]{2},\quad\text{and}\quad -i\sqrt[4]{2}.

In polar form, a single nth root may be found by the formula

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[n]{re^{i\theta}} \,=\, \sqrt[n]{r}\,e^{i\theta/n}.

Here r is the magnitude (the modulus, also called the absolute value) of the number whose root is to be taken; if the number can be written as a+bi then Failed to parse (Missing texvc executable; please see math/README to configure.): r=\sqrt{a^2+b^2} . Also, Failed to parse (Missing texvc executable; please see math/README to configure.): \theta

is the angle formed as one pivots on the origin counterclockwise from the positive horizontal axis to a ray going from the origin to the number; it has the properties that Failed to parse (Missing texvc executable; please see math/README to configure.): \cos \theta = a/r,
 Failed to parse (Missing texvc executable; please see math/README to configure.):  \sin \theta = b/r,
and Failed to parse (Missing texvc executable; please see math/README to configure.):  \tan \theta = b/a.

Thus finding nth roots in the complex plane can be segmented into two steps. First, the magnitude of all the nth roots is the nth root of the magnitude of the original number. Second, the direction of a ray from the origin to one of the nth roots involves an angle Failed to parse (Missing texvc executable; please see math/README to configure.): \theta / n

relative to the positive horizontal axis that is 1/n times the angle Failed to parse (Missing texvc executable; please see math/README to configure.): \theta
of a ray from the origin to the original number relative to the positive horizontal axis. Furthermore, all n of the nth roots are at equally spaced angles from each other.

As with square roots, the formula above cannot be applied consistently to the entire complex plane, but instead leads to a branch cut at the points where θ / n suddenly “jumps”.^{[clarification needed]}

Solving polynomials[link]

It was once believed that all roots of polynomials could be expressed in terms of radicals and elementary operations; however, while this is true for third degree polynomials (cubics) and fourth degree polynomials (quartics), the Abel-Ruffini theorem (1824) shows that this is not true in general when the degree is 5 or greater. For example, the solutions of the equation

Failed to parse (Missing texvc executable; please see math/README to configure.): x^5=x+1\,

cannot be expressed in terms of radicals. (cf. quintic equation)

For solving any equation of the nth degree numerically, to obtain a result that is arbitrarily close to being exact, see Root-finding algorithm.

See also[link]

• Nth root algorithm
• Shifting nth-root algorithm
• Irrational number
• Algebraic number
• Nested radical
• Twelfth root of two
• Super-root

References[link]

External links[link]

Look up surd in Wiktionary, the free dictionary.

Look up radical in Wiktionary, the free dictionary.

Look up nth in Wiktionary, the free dictionary.

The nth degree may refer to:

• The degree of a polynomial, where n represents a natural number
• "The Nth Degree" (Star Trek: The Next Generation)
• "Nth Degree" (song), a song by New York City band Morningwood
• A saying meaning that something is raised to a very high level (as in "to the Nth degree")
• An English saying referring to an unspecified term of a sequence

This disambiguation page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

Primary and secondary roots in a cotton plant

In vascular plants, the root is the organ of a plant that typically lies below the surface of the soil. This is not always the case, however, since a root can also be aerial (growing above the ground) or aerating (growing up above the ground or especially above water). Furthermore, a stem normally occurring below ground is not exceptional either (see rhizome). So, it is better to define root as a part of a plant body that bears no leaves, and therefore also lacks nodes. There are also important internal structural differences between stems and roots.

The first root that comes from a plant is called the radicle. The four major functions of roots are 1) absorption of water and inorganic nutrients, 2) anchoring of the plant body to the ground, and supporting it, 3) storage of food and nutrients, 4) vegetative reproduction. In response to the concentration of nutrients, roots also synthesise cytokinin, which acts as a signal as to how fast the shoots can grow. Roots often function in storage of food and nutrients. The roots of most vascular plant species enter into symbiosis with certain fungi to form mycorrhizas, and a large range of other organisms including bacteria also closely associate with roots.

Anatomy[link]

When dissected, the arrangement of the cells in a root is root hair, epidermis, epiblem, cortex, endodermis, pericycle and lastly the vascular tissue in the centre of a root to transport the water absorbed by the root to other places of the plant.

Root growth[link]

Early root growth is one of the functions of the apical meristem located near the tip of the root. The meristem cells more or less continuously divide, producing more meristem, root cap cells (these are sacrificed to protect the meristem), and undifferentiated root cells. The latter become the primary tissues of the root, first undergoing elongation, a process that pushes the root tip forward in the growing medium. Gradually these cells differentiate and mature into specialized cells of the root tissues.

Roots will generally grow in any direction where the correct environment of air, mineral nutrients and water exists to meet the plant's needs. Roots will not grow in dry soil. Over time, given the right conditions, roots can crack foundations, snap water lines, and lift sidewalks. At germination, roots grow downward due to gravitropism, the growth mechanism of plants that also causes the shoot to grow upward. In some plants (such as ivy), the "root" actually clings to walls and structures.

Growth from apical meristems is known as primary growth, which encompasses all elongation. Secondary growth encompasses all growth in diameter, a major component of woody plant tissues and many nonwoody plants. For example, storage roots of sweet potato have secondary growth but are not woody. Secondary growth occurs at the lateral meristems, namely the vascular cambium and cork cambium. The former forms secondary xylem and secondary phloem, while the latter forms the periderm.

In plants with secondary growth, the vascular cambium, originating between the xylem and the phloem, forms a cylinder of tissue along the stem and root. The vascular cambium forms new cells on both the inside and outside of the cambium cylinder, with those on the inside forming secondary xylem cells, and those on the outside forming secondary phloem cells. As secondary xylem accumulates, the "girth" (lateral dimensions) of the stem and root increases. As a result, tissues beyond the secondary phloem (including the epidermis and cortex, in many cases) tend to be pushed outward and are eventually "sloughed off" (shed).

At this point, the cork cambium begins to form the periderm, consisting of protective cork cells containing suberin. In roots, the cork cambium originates in the pericycle, a component of the vascular cylinder.

The vascular cambium produces new layers of secondary xylem annually. The xylem vessels are dead at maturity but are responsible for most water transport through the vascular tissue in stems and roots.

Types of roots[link]

This unreferenced section requires citations to ensure verifiability.

A true root system consists of a primary root and secondary roots (or lateral roots).

• the diffuse root system: the primary root is not dominant; the whole root system is fibrous and branches in all directions. Most common in monocots. The main function of the fibrous root is to anchor the plant.

Specialized roots[link]

Aerating roots of a mangrove

The growing tip of a fine root

The stilt roots of Socratea exorrhiza

The roots, or parts of roots, of many plant species have become specialized to serve adaptive purposes besides the two primary functions described in the introduction.

• Adventitious roots arise out-of-sequence from the more usual root formation of branches of a primary root, and instead originate from the stem, branches, leaves, or old woody roots. They commonly occur in monocots and pteridophytes, but also in many dicots, such as clover (Trifolium), ivy (Hedera), strawberry (Fragaria) and willow (Salix). Most aerial roots and stilt roots are adventitious. In some conifers adventitious roots can form the largest part of the root system.
• Aerating roots (or knee root or knee or pneumatophores or Cypress knee): roots rising above the ground, especially above water such as in some mangrove genera (Avicennia, Sonneratia). In some plants like Avicennia the erect roots have a large number of breathing pores for exchange of gases.
• Aerial roots: roots entirely above the ground, such as in ivy (Hedera) or in epiphytic orchids. They function as prop roots, as in maize or anchor roots or as the trunk in strangler fig.
• Contractile roots: they pull bulbs or corms of monocots, such as hyacinth and lily, and some taproots, such as dandelion, deeper in the soil through expanding radially and contracting longitudinally. They have a wrinkled surface.
• Coarse roots: Roots that have undergone secondary thickening and have a woody structure. These roots have some ability to absorb water and nutrients, but their main function is transport and to provide a structure to connect the smaller diameter, fine roots to the rest of the plant.
• Fine roots: Primary roots usually <2 mm diameter that have the function of water and nutrient uptake. They are often heavily branched and support mycorrhizas. These roots may be short lived, but are replaced by the plant in an ongoing process of root 'turnover'.
• Haustorial roots: roots of parasitic plants that can absorb water and nutrients from another plant, such as in mistletoe (Viscum album) and dodder.
• Propagative roots: roots that form adventitious buds that develop into aboveground shoots, termed suckers, which form new plants, as in Canada thistle, cherry and many others.
• Proteoid roots or cluster roots: dense clusters of rootlets of limited growth that develop under low phosphate or low iron conditions in Proteaceae and some plants from the following families Betulaceae, Casuarinaceae, Elaeagnaceae, Moraceae, Fabaceae and Myricaceae.
• Stilt roots: these are adventitious support roots, common among mangroves. They grow down from lateral branches, branching in the soil.
• Storage roots: these roots are modified for storage of food or water, such as carrots and beets. They include some taproots and tuberous roots.
• Structural roots: large roots that have undergone considerable secondary thickening and provide mechanical support to woody plants and trees.
• Surface roots: These proliferate close below the soil surface, exploiting water and easily available nutrients. Where conditions are close to optimum in the surface layers of soil, the growth of surface roots is encouraged and they commonly become the dominant roots.
• Tuberous roots: A portion of a root swells for food or water storage, e.g. sweet potato. A type of storage root distinct from taproot.

Rooting depths[link]

Cross section of a mango tree

The distribution of vascular plant roots within soil depends on plant form, the spatial and temporal availability of water and nutrients, and the physical properties of the soil. The deepest roots are generally found in deserts and temperate coniferous forests; the shallowest in tundra, boreal forest and temperate grasslands. The deepest observed living root, at least 60 m below the ground surface, was observed during the excavation of an open-pit mine in Arizona, USA. Some roots can grow as deep as the tree is high. The majority of roots on most plants are however found relatively close to the surface where nutrient availability and aeration are more favourable for growth. Rooting depth may be physically restricted by rock or compacted soil close below the surface, or by anaerobic soil conditions.

Rooting depth records[link]

Ficus Tree with very tall roots

Root architecture[link]

Tree roots at Cliffs of the Neuse State Park

The pattern of development of a root system is termed root architecture, and is important in providing a plant with a secure supply of nutrients and water as well as anchorage and support. The architecture of a root system can be considered in a similar way to above-ground architecture of a plant—i.e. in terms of the size, branching and distribution of the component parts. In roots, the architecture of fine roots and coarse roots can both be described by variation in topology and distribution of biomass within and between roots. Having a balanced architecture allows fine roots to exploit soil efficiently around a plant, but the plastic nature of root growth allows the plant to then concentrate its resources where nutrients and water are more easily available. A balanced coarse root architecture, with roots distributed relatively evenly around the stem base, is necessary to provide support to larger plants and trees.

Tree roots normally grow outward to about three times the branch spread. Only half of a tree's root system occurs between the trunk and the circumference of its canopy. Roots on one side of a tree normally supply the foliage on that same side of the tree. Thus when roots on one side of a tree are injured, the branches and leaves on that same side of the tree may die or wilt. For some trees however, such as the maple family, the effect of a root injury may show itself anywhere in the tree canopy.

Evolutionary history[link]

The fossil record of roots – or rather, infilled voids where roots rotted after death – spans back to the late Silurian,^[3] but their identification is difficult, because casts and molds of roots are so similar in appearance to animal burrows – although they can be discriminated on the basis of a range of features.^[4]

Economic importance[link]

Roots can also protect the environment by holding the soil to prevent soil erosion

The term root crops refers to any edible underground plant structure, but many root crops are actually stems, such as potato tubers. Edible roots include cassava, sweet potato, beet, carrot, rutabaga, turnip, parsnip, radish, yam and horseradish. Spices obtained from roots include sassafras, angelica, sarsaparilla and licorice.

Sugar beet is an important source of sugar. Yam roots are a source of estrogen compounds used in birth control pills. The fish poison and insecticide rotenone is obtained from roots of Lonchocarpus spp. Important medicines from roots are ginseng, aconite, ipecac, gentian and reserpine. Several legumes that have nitrogen-fixing root nodules are used as green manure crops, which provide nitrogen fertilizer for other crops when plowed under. Specialized bald cypress roots, termed knees, are sold as souvenirs, lamp bases and carved into folk art. Native Americans used the flexible roots of white spruce for basketry.

Tree roots can heave and destroy concrete sidewalks and crush or clog buried pipes. The aerial roots of strangler fig have damaged ancient Mayan temples in Central America and the temple of Angkor Wat in Cambodia.

Vegetative propagation of plants via cuttings depends on adventitious root formation. Hundreds of millions of plants are propagated via cuttings annually including chrysanthemum, poinsettia, carnation, ornamental shrubs and many houseplants.

Roots can also protect the environment by holding the soil to prevent soil erosion. This is especially important in areas such as sand dunes.

Roots on onion bulbs

See also[link]

• Rooting Powder
• Fibrous root system
• Mycorrhiza – root symbiosis in which individual hyphae extending from the mycelium of a fungus colonize the roots of a host plant.
• Rhizosphere – region of soil around the root influenced by root secretions and microorganisms present
• Root cutting
• Stolon
• Taproot
• Drought rhizogenesis
• Cypress knee

Notes[link]

References[link]

• Dennis D.Baldocchi and Liukang Xu. 2007. What limits evaporation from Mediterranean oak woodlands – The supply of moisture in the soil, physiological control by plants or the demand by the atmosphere? Vol 30, issue 10. Elsevier
• Brundrett, M. C. 2002. Coevolution of roots and mycorrhizas of land plants. New phytologist 154(2): 275–304. (Available online: DOI | Abstract | Full text (HTML) | Full text (PDF))
• Chen, R., E. Rosen, P. H. Masson. 1999. Gravitropism in Higher Plants. Plant Physiology 120 (2): 343–350. (Available online: Full text (HTML) | Full text (PDF)) – article about how the roots sense gravity.
• Clark, Lynn. 2004. Primary Root Structure and Development – lecture notes
• Coutts, M. P. 1987. Developmental processes in tree root systems. Canadian Journal of Forest Research 17: 761–767.
• Raven, J. A., D. Edwards. 2001. Roots: evolutionary origins and biogeochemical significance. Journal of Experimental Botany 52 (Suppl 1): 381–401. (Available online: Abstract | Full text (HTML) | Full text (PDF))
• Schenk, H. J., and R. B. Jackson. 2002. The global biogeography of roots. Ecological Monographs 72 (3): 311–328.
• Sutton, R. F., and R. W. Tinus. 1983. Root and root system terminology. Forest Science Monograph 24 pp 137.
• Phillips, W. S. 1963. Depth of roots in soil. Ecology 44 (2): 424.

External links[link]

Wikimedia Commons has media related to: Roots

• Botany – University of Arkansas at Little Rock
• Time-lapse photography of root growth

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