As we've commented on before in this blog, irrational numbers aren't really all that irrational. It is our representation of them that is irrational. The fact that we can't really write them down using normal numeric notation doesn't really mean there is anything complicated or nonsensical about the number itself. The most popular "irrational" number, π (even though we know that it really should be tau not pi that is popular), is nothing more than the ratio of the diameter of a circle to its circumference. That is a fairly simple concept, yet one that our numerical notation system can't really represent.
Well one of the unsung heros of the "irrational" number world is the square root of two. The video below shows both that this is a very useful number and that paper sizes in Europe are a lot more "rational" than paper sizes here in the US.