What is a transcendental number? I came across some numbers which were called transcendental numbers. What are they exactly I want with explanation and eg 
 A: Trancedental numbers are numbers which are not the zero of a polynomial with coefficients in $\Bbb Q$. Actually there is a notion of transcendental numbers over any field, but it is usually referring to $\Bbb Q$ when the field is not specified.
For example, $\sqrt{2}$ is not transcendental, since it is a zero of the polynomial $x^2-2$. On the other hand, both $e$ and $\pi$ are transcendental, a difficult thing to prove.
A: Transendental numbers are those numbers which are not the root of a non zero polynomial with integer coefficiants 
The most famous example of a transcendental number is $\pi$ 
$\sqrt2$ is an irrational number but is not transcendental as it is the solution of the equation $x^2-2 = 0 $
You might be wondering how to prove $\pi$ is transendental
It can be proved by contadiction, suppose $\pi$ is algebraic, then $\pi i$ will also be algebraic as $i$ is algebraic and by Lindemann–Weierstrass theorem, we know that $e^{\pi i} = -1$ will be transcendental which is a contradiction as this is the solution of the equation $x^2 -1 = 0$
