Transcendental Numbers (simple question)

Question

Are all transcendental numbers irrational? I know that not all irrationals are transcendental (for example, $\sqrt{2}$); but I only know of a few transcendental numbers and they are all irrational.

Answer 1

To compile what has been said above, any transcendental number must be irrational. As egreg mentions, it suffices to use the polynomial $p(x) = bx-a$ for any rational number $a/b$. Note the definition of "transcendental:" A number is transcendental if it is not the root of any nonzero polynomial with rational coefficients. Hence we have shown that indeed any rational number is algebraic, that is, not transcendental.