Abarim Publications' online Biblical Hebrew Dictionary
There are three different roots of the form בער (b'r) in the Bible, and these are formally separated. To a Hebrew audience, and especially the Hebrew poets who wrote the Bible, the similarities were probably much more compelling than the differences:
The verb בער (ba'ar I), means to kindle, burn or consume. It should be noted that in Biblical times a fire was the center of civilization. People gathered around it, cooked on it, kept wild animals at bay with it and purified their metals with it. A possible negative usage of this verb is in the action of burning with anger or intense emotion (Esther 1:12, Jeremiah 20:9).
The obvious derivation of this verb is בערה (be'era), meaning fire (Exodus 22:6), but it must be noted that this is a very rare form, literally meaning "that what was kindled".
Curiously, another verb that is identical to the one mentioned above, is בער (ba'ar II), meaning to be stupid, brutish or most literally: beastly. This verb was probably formed after the noun בעיר (be'ir), denoting beasts or cattle.
BDB Theological Dictionary deems the connection between the two verbs obscure, and perhaps the two verbs came to the Hebrew language via other languages and accidentally became identical. But perhaps the Hebrews recognized anger, and especially acts committed out of anger, to be behavior shared with higher animals. HAW Theological Wordbook of the Old Testament reads about the latter root, "The root seems to contrast man's ability to reason and understand with the beast's inability to do so - Proverbs 30:2".
But then, language such as used in Exodus 22:4-6 shows these two roots side by side, once as cattle that grazes clean a field, and then as fire that does the same to stacks of grain.
The Hebrew verb בער (ba'ar III) was, until recently, considered part of (ba'ar I) but lately it is viewed separately (or so sayeth HAW Theological Wordbook of the Old Testament). This is, of course, tremendously clever, but one may wonder if the Hebrews themselves knew about this.
This completely separate root בער (ba'ar III) occurs twenty-seven times and mostly denotes a removal of evil from the land. That this removal became typically depicted as purification by fire has apparently no bearing on the discussion of where this separate root came from. Here at Abarim Publications, we doubt that there are indeed three separate roots.