How can we use irrational numbers in math if we don’t know the full number?

Question

How can we use irrational numbers in math if we don’t know the full number?

In: 232

Answer 1

We still know enough about the number to do useful things.

Eg, the square root of 2 is irrational. We know it squares to 2. From that, we can figure out that the square root of 2 is between 1.41421 and 1.41422, so if I want to cut a piece of wood to a length of sqrt(2) metres, I can do so to way better than millimeter precision. If I need better precision still, I can always work out more decimal places of sqrt(2).