Are all normal numbers transcendental?

Question

Are all normal numbers transcendental?

Just a question I've come up with.

Answer 1

I found this on Wikipedia:

It has been conjectured that every irrational algebraic number is normal; while no counterexamples are known, there also exists no algebraic number that has been proven to be normal in any base.

So while this does not answer your queston, it shows that the answer is not that simple ...