k-d-sh — to be set apart, to be holy
ק.ד.ש (kadash) does not mean pure or good — it means separated, reserved, marked off for one purpose. Kiddush, Kaddish, mikdash and Jewish betrothal all come from it.
The word family
Every word below is built on ק.ד.ש. Same three letters, different vowels and prefixes.
Marriage as setting one person apart for another — the same verb used for consecrating an offering.
בֵּית הַמִּקְדָּשׁ (Beit ha-Mikdash) — the Temple in Jerusalem.
Aramaic, not Hebrew — which is why it is kaddish and not kadosh.
In the text
קְדֹשִׁים תִּהְיוּ כִּי קָדוֹשׁ אֲנִי
Kedoshim tihyu ki kadosh ani
You shall be holy, for I am holy.
What I tell students about this root
Translate kadosh as "holy" and you import an English sense of moral purity that the Hebrew does not carry. The root idea is separation — this thing is not available for ordinary use. That is why the same verb betroths a spouse and consecrates an altar, and why the opposite of kadosh is not "sinful" but חוֹל (chol), "ordinary".