Rashly and the adjective rash come from a root meaning "flash of lightning." Make decisions as quick as lightning, and you make them rashly.
What does rashness mean?
acting or tending to act too hastily or without due consideration. characterized by or showing too great haste or lack of consideration: rash promises.
Where did rashes come from?
The noun "rash," which first appeared in English in the 1700s, comes by way of French and Vulgar Latin from Latin rasus, the past participle of "radere" ("to scrape" or "to shave").