Is beau rootword of beautiful

No - the Word is beauteous and it has both good and bad meanings. The Dictionary.com meaning is: Full of beauty; beautiful; very handsome.

But some people think it is a combination of beautiful and hideous - the slang meaning from the Urban Dictionary is ugly, but in a unique, appealing, and/or interesting way.

HOWEVER, the spelling 'beautious' is a valid early spelling, and is encountered as late as 1700.