Does allege have a root word?

Yes, the word "allege" has a root word, which is the Latin word "allegare", meaning "to attach, to bind, to assign".

"Allegare" itself derives from the Latin word "ligare", meaning "to bind".

So, the chain of etymology goes:

* ligare (Latin) - to bind

* allegare (Latin) - to attach, to bind, to assign

* allege (English) - to assert without proof

Therefore, the original meaning of "allege" is related to the idea of attaching or associating something to another thing, which evolved to mean "to claim or assert something without proof."