Why a segment of length $\sqrt{2}$ can be drawn but a segment of length $\pi$ cannot?

Question

We know that both $\pi$ and $\sqrt{2}$ are irrational. Also, it has been proved that a segment of length $\pi$ can not be drawn whereas a segment of length $\sqrt{2}$ can be drawn. Why is it so, though both are irrational?

Answer 1

root(2) is the length of the diagonal of a square which which side is 1. root(2) is algebraic it is the root of $x^2-2$ and

$\pi$ is not algebraic, it is transcendantal, remark that $\pi$ is the perimeter of a circle of radius 1/2

Answer 2

If you define "drawing" a number as being able to construct it with ruler and compass, $\sqrt{2}$ can be drawn, while $\pi$ can't. But $\sqrt[3]{2}$ can't be drawn either. In fact, in some sense the overwhelming majority of numbers can't be drawn.