The very first words out of my mouth need to be this... "Solving" is the wrong term since I am speaking about irrational numbers. I just don't know which word is the correct word... So that can be part 1 of my question... what is the correct word since you obviously can't "solve" an irrational number because it goes forever.
Part 2 (my real question) are there algorithms for figuring out the answer to a problem like the square root of 2 other than guess-and-checking your way to infinity? Again, I'm obviously not asking for an algorithm to give me the never ending answer because that's crazy... but for example if I wanted to know what the 15th decimal place of the square root of 2 was, is there an algorithm for that?
Thankyou! (I'm new here and know nothing about how to format math questions so any help or links would be appreciated as well, thanks!)