ש.ל.ם
sh-l-m — to be whole, complete
ש.ל.ם (shalem) means whole, not calm. Shalom, paying a bill, finishing a task and the name Jerusalem all sit on this root.
Biblical HebrewModern Hebrew
The word family
Every word below is built on ש.ל.ם. Same three letters, different vowels and prefixes.
שָׁלוֹםshalomnoun
peace, wholeness; hello, goodbye
שָׁלֵםshalemadjective
whole, complete, intact
שִׁלֵּםshilemPi'el
paid
Paying is completing — you make the transaction whole.
תַּשְׁלוּםtashlumnoun
payment, instalment
הִשְׁלִיםhishlimHif'il
completed; made peace with
מוּשְׁלָםmushlamHuf'al participle
perfect
יְרוּשָׁלַיִםYerushalayimplace name
Jerusalem
The second half carries this root. The traditional reading is a city of wholeness.
What I tell students about this root
Shalom as a greeting is not wishing someone a quiet life. The root is completeness, so the question מַה שְׁלוֹמְךָ? (mah shlomkha?) literally asks what your wholeness is — how intact you are. That is a rather more searching "how are you" than the English one.