This root sits exactly where the mind meets math. To think (לַחְשֹׁב) and to calculate (לְחַשֵּׁב) are the same three letters: weighing things in the head. From there the family spreads two ways. One way is the machine: machshev (computer), machshevon (calculator), the thing that thinks for you. The other is the ledger: cheshbon (account, bill), cheshbonit (invoice). What you esteem (לְהַחְשִׁיב) is literally what you count as mattering. 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 three binyanim split one idea cleanly: pa'al is plain thinking, pi'el is intensive thinking turned into calculation, and hif'il is causative: to make something count, to deem it important. The reflexive hitpa'el survives only inside the noun הִתְחַשְּׁבוּת (consideration for others). The passive partners are not lexicalized.
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.