1. The problem statement, all variables and given/known data 0 < a < b Must prove that a < sqrt(ab) < (a+b)/2 < b 2. Relevant equations Well, relevant info. I am using Spivak's calculus book, where we have to prove everything. 3. The attempt at a solution I'm not sure if I'm doing this right but here's my start. I'll start with a < b. Multiply both sides by a, and you get a times a < a times b. Then you get a^2 < ab Then square root of a^2 < square root of ab. a < square root of ab. So I think i have the first part of that, but I'm not sure where to start for a+b/2?