Hi.

End of semester cram time. Professor snuck in the definition of an algebraic number in our assignment.

I have been able to figure out that

$\displaystyle 6 + \sqrt[4]{2}$

is an algebraic number because it is a root of $\displaystyle (x-6)^4-2$

What about something like:

$\displaystyle \sqrt{2} + \sqrt{-7}$

$\displaystyle (x)^2+7 $ and $\displaystyle (x)^2-2$

Then, my mind goes numb on how to put those together.

Please help.

Thank you.