Three consonants carry one idea: seeking and requiring. To seek hard enough is to demand; to seek meaning in a text is to interpret it. From this come the requirement that must be met, the thing that is wanted, the rabbinic midrash that digs meaning out of Scripture, and the school where that digging is taught. One act of insistent searching, splitting into law, longing, and study. 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 pa'al spans a wide arc: at one end, to demand or require; at the other, to seek out and expound a meaning (this is the verb behind midrash). The nif'al is its passive, what is sought of you becomes what is required. Other binyanim are not lexicalized for this root.
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.