RADICAND - translation to arabic
Diclib.com
ChatGPT AI Dictionary
Enter a word or phrase in any language 👆
Language:

Translation and analysis of words by ChatGPT artificial intelligence

On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:

  • how the word is used
  • frequency of use
  • it is used more often in oral or written speech
  • word translation options
  • usage examples (several phrases with translation)
  • etymology

RADICAND - translation to arabic

FUNCTION
Surds and Indices; Surds and indices; Radicand; Nth root algorithm; Nth-root algorithm; Properties of radicals; N-th root; Radical root; N-th root algorithm; Nth roots; Fourth root; Fifth root; Sixth root; Surd (mathematics); Radical expression; ؇; Root extraction; Radical signs; Principal root; Radication; 3-root; Twelfth root; Eleventh root; Tenth root; Ninth root; Eighth root; Seventh root; Nth root extraction
  • The three 3rd roots of 1
  • The three 3rd roots of −1,<br /> one of which is a negative real
  • The four 4th roots of −1,<br /> none of which are real

RADICAND         

ألاسم

مَجْذُور

الصفة

ثائِر ; ثَوْرِيّ ; رادِيكالِيّ ; غالٍ ; غَلِيّ ; مُتَطَرِّف ; مُتَهَوِّر

radicand         
المجذور
root extraction         
قَلْعُ الجَذْر

Definition

Radication
·noun The disposition of the roots of a plant.
II. Radication ·noun The process of taking root, or state of being rooted; as, the radication of habits.

Wikipedia

Nth root

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

r n = x , {\displaystyle r^{n}=x,}

where n is a positive integer, sometimes called 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 by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an nth root is a root extraction.

For example, 3 is a square root of 9, since 32 = 9, and −3 is also a square root of 9, since (−3)2 = 9.

Any non-zero number considered as a complex number has n different complex nth roots, including the real ones (at most two). The nth root of 0 is zero for all positive integers n, since 0n = 0. In particular, if n is even and x is a positive real number, one of its nth roots is real and positive, one is negative, and the others (when n > 2) are non-real complex numbers; if n is even and x is a negative real number, none of the nth roots is real. If n is odd and x is real, one nth root is real and has the same sign as x, while the other (n – 1) roots are not real. Finally, if x is not real, then none of its nth roots are real.

Roots of real numbers are usually written using the radical symbol or radix       {\displaystyle {\sqrt {{~^{~}}^{~}\!\!}}} , with x {\displaystyle {\sqrt {x}}} denoting the positive square root of x if x is positive; for higher roots, x n {\displaystyle {\sqrt[{n}]{x}}} denotes the real nth root if n is odd, and the positive nth root if n is even and x is positive. In the other cases, the symbol is not commonly used as being ambiguous. In the expression x n {\displaystyle {\sqrt[{n}]{x}}} , the integer n is called the index and x is called the radicand.

When complex nth roots are considered, it is often useful to choose one of the roots, called principal root, as a principal value. The common choice is to choose the principal nth root of x as the nth root with the greatest real part, and when there are two (for x real and negative), the one with a positive imaginary part. This makes the nth root a function that is real and positive for x real and positive, and is continuous in the whole complex plane, except for values of x that are real and negative.

A difficulty with this choice is that, for a negative real number and an odd index, the principal nth root is not the real one. For example, 8 {\displaystyle -8} has three cube roots, 2 {\displaystyle -2} , 1 + i 3 {\displaystyle 1+i{\sqrt {3}}} and 1 i 3 . {\displaystyle 1-i{\sqrt {3}}.} The real cube root is 2 {\displaystyle -2} and the principal cube root is 1 + i 3 . {\displaystyle 1+i{\sqrt {3}}.}

An unresolved root, especially one using the radical symbol, is sometimes referred to as a surd or a radical. Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called a radical expression, and if it contains no transcendental functions or transcendental numbers it is called an algebraic expression.

Roots can also be defined as special cases of exponentiation, where the exponent is a fraction:

x n = x 1 / n . {\displaystyle {\sqrt[{n}]{x}}=x^{1/n}.}

Roots are used for determining the radius of convergence of a power series with the root test. The nth roots of 1 are called roots of unity and play a fundamental role in various areas of mathematics, such as number theory, theory of equations, and Fourier transform.