Day Eight will make you think a second ... or ten.
(if they don't know the 3D Pythagorean theorem and have to work it out.)
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 8 and answer 34.