2007: 9 and 33

Day Nine.

Difficulty: easy-ish.

Number 33: 

Difficulty: Hard.
(or as the kids said, OMFG)
It's actually more complicated than hard.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 9 and answer 33.