One root, two faces that turn out to be one. On one side it means to approve, confirm, make valid; on the other it means happiness, bliss. The thread between them is old: to be "set right, made firm" is both what an official does to a document and what a fortunate person feels inside. The same letters give you the visa stamp on your passport and the word for being content. 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.
Only the intensive pi'el is in everyday use as a verb; the "happiness" side of the root lives in nouns and adjectives, not in a separate verb. The passive partner pu'al shows up frozen in the adjective מְאֻשָּׁר ("made happy").
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.