This is a geminate root: its last two letters are the same (ר־ר), and the original idea is sorting, picking the good from the bad, like sifting grain. From sorting comes clarity: once you have separated things out, the matter is clear. So the pa'al picks, the pi'el clarifies and finds out, and the family gives you what is obvious, an investigation, and the leftover when sorting leaves you only one option. 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.
Because the root is geminate (the doubled ר), its forms look a little compressed: the pa'al לָבֹר contracts to one syllable. The everyday verb is the pi'el לְבָרֵר, "to find out / clarify", which is what you do at a counter when you ask them to look into your case.
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.