Arithmetical root

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  is called 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”.