Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic
Prove that if a is a natural number and the square root of a is
rational, then it is a square number (an integer n^2 for some
Solve quadratic equations and use continued fractions to find
rational approximations to irrational numbers.
See the problem The
Root Cause .
Try to apply this method and then to extend it to three
variables for the last part.