Note: Q is rational numbers, R is real numbers ,
sqrt() means square root
Show that Q(sqrt(2)) is the smallest subfield of R that contains sqrt(2).
First, Q(sqrt(2)) is a subfield of R. An arbitrary element in Q(sqrt(2)) has the form x=a+bsqrt(2) with a,b in Q. We note ...
A proof involving rational and real numbers is provided.