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1. The problem statement, all variables and given/known data

What are the smallest subfields of R containing Zand Z[[tex]\sqrt{2}[/tex]]?

2. Relevant equations

Z= {a+ib|a,b[tex]\in Z[/tex]}

Z[[tex]\sqrt{2}[/tex]]={a+b[tex]\sqrt{2}[/tex]|a,b[tex]\in Z[/tex]}

3. The attempt at a solution

Z[tex]\subset[/tex]Qand Z[[tex]\sqrt{2}[/tex]][tex]\subset[/tex]Q[[tex]\sqrt{2}[/tex]]

so to get the subfield that contains both of them, would it be Q[i,[tex]\sqrt{2}[/tex]]?

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# Homework Help: Smallest subfields containing Z and Z[sqrt2]

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