Prove that for $x^3=3$ there isn't rational solution
What I did:
Suppose $x= u /v$ is solution
$$\left(\frac u v\right)^3=3$$
Let's take third root from both sides:
$$\frac u v =\sqrt3$$
and $\sqrt3$ is irrationl ,
my problem is this "and $\sqrt3$ is irrationl " is it well known that this number is irrationl? same as $\pi$?
or maybe there is another why to prove it?