Mislaid and mislay use the "bad or wrong" prefix mis-, along with lay or laid, "put down."

Is mislay a prefix?

Mislay implies that you've put the lost object down somewhere, and you'll find it again soon. The word adds the "bad" or "wrong" prefix mis- to lay, from the Old English lecgan, "to place on the ground."

What is the root word of misplaced?

The root word in misplaced is place; 'mis' is a prefix and 'ed' is a suffix.