The extended study of 2-refined neutrosophic numbers

Numerical roots play a crucial role in real or complex equations, as well as in various mathematical models involving differentiation, integration, and other mathematical relationships. In the realm of mathematics, there is a growing trend of utilizing new formulas that incorporate non-classical numbers, such as neutrosophic and refined neutrosophic numbers. The objective of this research is to establish precise and comprehensive mathematical procedures for dealing with refined neutrosophic roots within mathematical formulas, be it equations or other mathematical constructs. This paper presents an extensive study on 2-refined neutrosophic numbers, focusing on the square root of a 2-refined neutrosophic real or complex number. Additionally, this work introduces the concept of 2-refined neutrosophic real or complex polynomials and explores the process of finding the refined neutrosophic roots to solve 2-refined neutrosophic equations. To illustrate these concepts, several examples have been provided.