The value you have gotten is correct for the question asked.
Easy way to check would be to sub in your 'r' value in the eqn 'g = GM/r^2'
Your r value comes out to a g of around 0.098 (which is 0.01 of g on earth)
Their r value comes out to a g of around 9.268. WRONG.
I did the working and got the same answer as you, I also tried a different method and still got the same answer. I think you're right the book must be mistaken.
YeaI got the same answer... and everything you did looks right . Need another person to determine if the book is wrong again