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Arithmetical root

Arithmetical root. Algebraic root.
Absolute value (modulus) of number.

As we know, an even degree root has two values: positive and negative, so

An arithmetical root of the n-th degree of a non-negative number  a  is called a non-negative number, the n-th power of which is equal to  a .

An algebraic root of the n-th degree of a given number  a  iscalled a set of all roots of this number. An algebraic root of an even degree has the two values:positive and negative, for instance:

An algebraic root of an odd degrees has a single value: either positive, or negative.For example, the arithmetical root

Unlike this, the cube degree root:

An arithmetical root is closely connected with the notion of an absolute value(modulus) of number, exactly:

Operations with roots in more detail see the section “Powers and roots”.


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