Three consonants carry one idea: seeing. The plain verb sees; the passive is visible or seems; the causative shows; the reciprocal is two people seeing each other again, the everyday goodbye lehitra'ot. The nouns then name what seeing produces: the eyesight itself, the mirror that throws sight back, the proof that makes a claim visible to reason, even the interview where two people size each other up. 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.
Four binyanim are live and map cleanly onto voice: pa'al sees, nif'al is seen/seems, hif'il causes seeing (shows), hitpa'el is reciprocal (see each other). The pi'el, pu'al and huf'al slots 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.