What is the root for word a?

The word "a" is not a word with a root in the traditional sense. It's a definite article, a word that precedes a noun to specify which one is being referred to.

It doesn't have a root because it's a basic, unanalyzable word in the English language.

However, it's worth noting that the word "a" is related to other words, like the number "one" and the indefinite article "an." These words share a common ancestor in Proto-Indo-European, but "a" itself doesn't have a specific root that can be traced back to that ancestor.