In the beginning, there was RedHat. Some French guys tasted RedHat, and found it not to their liking - they wanted KDE, yet RedHat shunned KDE in favour of their chosen desktop: Gnome. And lo, Mandrake was born - it was like Red Hat, but with KDE.
Fast-forwarding to today, they both have many of the same features (redhat now includes kde as well as gnome), but they've been developed by different people for the last few years, so there are differences.
If there are two distros that are the most similar, it's probably RH and Mdk. They're not identical, but if you show a little intelligent flexibility, your redhat book should be fine with mandrake.
Having said that, if you've got both, you might as well install redhat for your initial 'learning experience', so that your book can hand-hold you. If you later decide that you want to give mandrake a try, then there'll be nothing stopping you. Mandrake is a more newbie friendly distro in most people's opinion, but my advice would be to play safe and go with the one that you've got a mass of dead-tree about.
Just make sure that your book covers a recent version of Redhat (7 or above). If the book's out of date, you're better off with mandrake.