Actually, Pi and e are not just irrational numbers - they are transcendental numbers. They are not the roots of any algebraic equation. Numbers - like root 2, root 3 etc are irrational, they are the roots of 'simple' equations.

It is a moot point s to whether there are, in fact, more rational than irrational numbers. Just 'cos we can think of more doesn't mean there are more.

Pi, e and others, come from more complex equations, involving trigonometry, integration, logarithms, etc.