Do chastity and chastise have the same root?

Yes, both chastity and chastise have the same root, which is the Latin word "castitas".

* Chastity is derived from "castitas" and means sexual purity or abstinence.

* Chastise is derived from "castigare", which itself is derived from "castitas". "Castigare" means to punish or discipline, and it originally referred to the act of making someone pure or morally upright.

So, while they have different meanings today, they share the same root and concept of purity or moral rectitude.