1. The problem statement, all variables and given/known data I am asked to discover and prove the inequality relationship between root mean square, arithmetic mean, geometric mean, and harmonic mean. 2. Relevant equations Let a,b, be non-negative integers. (a-b)2 ≥ 0 and (√a-√b)2 ≥ 0 3. The attempt at a solution Using (a-b)2 ≥ 0 and (√a-√b)2 ≥ 0, I was able to show that AM ≥ GM , GM ≥ HM, and RMS ≥ GM, but I haven't really been able to show that RMS ≥ AM and I was wondering if someone could point me in the right direction. I used (a-b)2 ≥ 0 and did some algebra to show that √((a2+b2)/2) ≥ √ab But I don't know if I can use that to show RMS ≥ AM. Thanks in advance to anyone who can offer some insight.