Can anyone teach me a little bit about p-adic expansion? especially the case where we have to expand a square root.
Perhaps reading about it will help?
p-adic Expansions
HugeDomains.com - Shop for over 350,000 Premium Domains (A Tutorial on p-adic Arithmetic C¸ . K. Ko¸c Electrical & Computer Engineering Oregon State University Corvallis, Oregon 97331 Technical Report, April 2002) It's a .pdf file
p-adic Number -- from Wolfram MathWorld
If it's the square root of a p-adic integer, http://deltaepsilons.files.wordpress.../09/p-adic.pdf might be able to help, specifically slide 12.