# Integral Domains, Fields and Subfields

Not what you're looking for? Search our solutions OR ask your own Custom question.

Problem:

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).

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:54 pm ad1c9bdddfhttps://brainmass.com/math/integrals/integral-domains-fields-subfields-17276

#### Solution Preview

Proof:

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 ...

#### Solution Summary

A proof involving rational and real numbers is provided.

$2.49