“Should I memorize the sides so I don’t have to hold the pages?”
No. I don’t think you should. I give this opinion after having gone through many, many auditions, reading Shurtleff’s Audition, and studying with Richard Brestoff. I think there is more (potential) harm in NOT holding the pages. Holding the pages also tells the auditors that “this is a work in progress, not a final product,” which might help you.
Yes, you DO memorize monologues and DO NOT hold the pages then, but this post is not about monologues.