The word radical refers to “roots” and “origins.” When leftists talk about “radical solutions,” we mean viewing problems of inequality as consequences of systems, then identifying and changing the fundamental nature of those systems.
I find it helpful to picture a literal root, like that of a plant. In order to fully evaluate and understand the plant as an entire organism, a system of gathering, manipulating, and distributing resources to sustain itself, one needs to expose the roots of the plant. The hidden origins of the visible.
The conflation of the term “radical” with “extremist” is fallacious. Extremism proposes simple answers to complex problems. An extremist solution to wealth inequality might sound like: “Well, if rich people are the problem, let’s just kill all of the rich people and take their money.” A radical evaluation of wealth inequality might say: “Let’s look at how wealth is created, controlled, and distributed, as a system, and see where the inequalities develop.”