What is the word root of impercetibly?

The word root of "imperceptibly" is percipere, which is a Latin verb meaning "to perceive".

Here's how the word is built:

* percipere (Latin verb) + -ible (suffix meaning "capable of being") = perceptible

* im- (prefix meaning "not") + perceptible = imperceptible

So, "imperceptibly" means "in a way that cannot be perceived."