with respect of xsolve y=sqareroot of x, using the first principle.

See following sites for detailed description of the longhand manual method.

http://www.homeschoolmath.net/teaching/square-root-algorithm.php
http://mathforum.org/library/drmath/view/52610.html

See also the numerous references at:
http://www.jiskha.com/display.cgi?id=1249308939