The extraction of roots

Definitions

  • Webster's Revised Unabridged Dictionary
    • The extraction of roots (Math) The operation of finding the root of a given number or quantity.
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Usage

In literature:

With most of his clients he would have contented himself with the extraction of the loose tooth and the roots of the broken one.
"McTeague" by Frank Norris
And in that case any further calculation becomes a mere matter of the extraction of a root.
"Frenzied Fiction" by Stephen Leacock
Extract the fourth root of the quotient, which is the thickness in inches.
"A Catechism of the Steam Engine" by John Bourne
How do you extract the square of a Beet-root?
"Punch, or the London Charivari, Volume 100, May 9, 1891" by Various
Who can extract the cube root of an ash-tree?
"Tragic Sense Of Life" by Miguel de Unamuno
The chiefs constantly begin their meal with a dose of the extract of pepper-root, brewed after the usual manner.
"A General History and Collection of Voyages and Travels, Volume 17" by Robert Kerr
Extract the root of Mr. Roebuck's family tree, and say whether it would come out in anything but vulgar fractions.
"Punch, or the London Charivari, Volume 1, Complete" by Various
A number of examples follow for squaring and the extraction of square root.
"Instruction for Using a Slide Rule" by W. Stanley
He would extract the cube root of nine figures in a few seconds (1804- ).
"Character Sketches of Romance, Fiction and the Drama" by E. Cobham Brewer
When the crown of the tooth has been destroyed and only the stump or root is left, extraction is impracticable.
"Special Report on Diseases of Cattle" by U.S. Department of Agriculture
The poison used by the Bushmen is extracted from the serpent's bag, from the root of the agapanthus, lily, and other plants.
"The Cape and the Kaffirs" by Harriet Ward
The roots of the original equation are then finally determined by the extraction of a fifth root.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6" by Various
Of the root one drachm, of the tincture one drachm, and of the alcoholic extract four grains, have caused death.
"Memoranda on Poisons" by Thomas Hawkes Tanner
He mentally extracted the cube root of 268,336,125; and the squares of 244,999,755 and 1,224,998,755.
"Memory" by William Walker Atkinson
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In poetry:

Who plants a seed begets a bud,
Extract of that same root;
Why marvel at the hectic blood
That flushes this wild fruit?
"Fruit Of The Flower" by Countee Cullen

In news:

As a result of this design, the forceps were positioned around an existing bridge, allowing extraction of this tooth root without affecting the integrity of the bridge itself.
Thus it would be possible to extract a tooth root without affecting the integrity of the bridge itself.
Extracted from the root bark of the tabernathe iboga plant, ibogaine is a potent hallucinogen —with an intriguing side effect.
Over 300 human studies on Rhodiola rosea show that the plant has anti-stress, anti-anxiety, and anti-depressant properties, and that taking the extract of the root produces no significant negative effects.
Therefore, when measuring the output of an orifice plate meter, a venturi meter, or pitot tube, square root extraction is necessary to linearize the output for use in the control system.
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In science:

The root singularity in the right hand side of Eq. (41) can be extracted using the formulae derived in the appendix of Ref. .
General Covariance in Quantum Gravity
In [HK-T], the authors extract some basic properties of GRLAs from the axioms, but for the further study of such Lie algebras they assume the irreducibility of the corresponding root systems.
Generalized reductive Lie algberas
Let D denote the set of the class of groups in which extraction of roots is always uniquely possible.
On the residual solvability of generalized free products of finitely generated nilpotent groups
One can also extract the exponents from the root space decomposition of G.
Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices
I is the unity matrix with the dimension of zero grading subspace: the notation MR means that from the algebra valued function M necessary extract coefficient under corresponding root R of the algebra belonging to grading spaces with indexes ±2, ±1 and 0.
Two Poisson structures invariant with respect to discrete transformation in the case of arbitrary semi-simple algebras
For this tiling model however, some of the roots of the BA equations almost coincide, which makes it difficult to extract high precision data.
Bethe Ansatz solution of a decagonal rectangle triangle random tiling
As we shall see below, this is exactly what happens, when one extracts the necessary root of the abelian theory treated in , so as to get the right scaling of the curvature.
Geometric construction of modular functors from Conformal Field Theory
Extracting cubic roots from all entries of M one gets the Hasse–Witt/Cartier– Manin matrix M (3) of C (with respect to the standard basis in the space of differentials of the first kind) , , [5, p. 129].
Non-supersingular Hyperelliptic jacobians
Fourth root of the topological susceptibility c carried by center projection vortices, in units of the square root of the string tension s, simultaneously extracted from the center projected lattice ensemble.
Susceptibility of Monte-Carlo Generated Projected Vortices
The determination of the root-mean-square (rms) radii requires the extraction of the nuclear form factor F (q2 ) from the angular distributions.
Nuclear mass form factors from coherent photoproduction of $\pi^0$ mesons
Root-mean-square radii of the mass distributions have been extracted in two different ways.
Nuclear mass form factors from coherent photoproduction of $\pi^0$ mesons
For example, extracting sets of nodes, or evaluating XPath expressions relative to the root naturally give rise to unary queries.
Logics for Unranked Trees: An Overview
Given a smooth curve C , defined over a field of characteristic p, with function field L(C ), we let L(C )1/p be the field obtained by extracting pth roots of L(C ) in some fixed algebraic closure.
A Theory of Divisors for Algebraic Curves
The statistical error was extracted from a ROOT fit of the Mℓℓ distribution and we estimate the theoretical accuracy to be of the order of 1%.
The MSSM with decoupled scalars at the LHC
Accurate determination of these quantities in combinations with the corresponding measurements can be used to extract the relative root mean square (rms) nuclear charge radii of different isotopes that cannot be measured directly [3, 5].
Studies of all order correlation effects in the isotope shifts and fine structure variation constants: Applications to Na and Mg+
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