What is the definition of a radical number in math?

1 Answer
Sep 19, 2015

Answer:

A normal radical is a root of a polynomial of the form #x^n - a = 0#

If #n = 2# then we call #x# a square root of #a#

If #n = 3# then we call #x# a cube root of #a#

Explanation:

Normal radicals are otherwise known as #n#th roots.

If #a >= 0# then #x^n - a = 0# will have a positive Real root known as the principal #n#th root, written #root(n)(a)#.

If #n# is even, then #-root(n)(a)# will also be an #n#th root of #a#.

If a polynomial is of degree #<= 4# then its zeros can be found and expressed using just normal radicals: square roots and cube roots. (Note that fourth roots are just square roots of square roots).

If a polynomial is of degree #5# - a quintic, then its roots may not be expressible in terms of normal radicals.

To get beyond this limitation, the Bring radical is a root of the polynomial equation #x^5+x+a = 0#

It is possible to reduce any quintic equation to a form (Bring-Jerrard normal form) that only has terms in #x^5#, #x# and a constant term, and hence to express its roots in terms of a Bring radical.