# Determine whether this is a subfield of R

1. Mar 1, 2008

### dash

Let Q denote the field of rational numbers and R denote the field of real numbers. Determine whether or not set S = {r + s√2 | r, s € Q} is a subfield of R.

Last edited: Mar 1, 2008
2. Mar 1, 2008

### Dick

Belong to quotient of what? That's not very grammatical.

3. Mar 1, 2008

### dash

Let Q denote the field of rational numbers and R denote the field of real numbers. Determine whether or not set S = {r + s√2 | r, s € Q} is a subfield of R.

4. Mar 2, 2008

### Dick

That's better. Just show S is closed under the field axioms. The big question is if a and b are in S is a/b in S? If b=r+sqrt(2)s it's useful to multiply the numerator and denominator of a/b by (r-sqrt(2)s).