At the heart of this root sits a single act: to judge, to weigh a case and rule on it. From it Hebrew builds the law itself (דִּין), the one who judges (דַּיָּן), the debate before the ruling (דִּיּוּן), and, remarkably, the state (מְדִינָה), a territory ruled under one law. The middle י can hide and reappear, so the family looks varied while sharing one judicial spine. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
The living verb here is the hitpa'el, whose reciprocal force fits judgment perfectly: two sides arguing a case before a ruling. The plain pa'al "to judge" (לָדוּן) belongs to the related root ד־ו־ן; everyday Modern Hebrew leans on the hitpa'el and on the rich noun family.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.