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 usually can get rid of them later eg. squaring square roots, dividing by the same irrational number etc. You can think of it as letters in your equations.

They also represent various truths in geometry like the Pythagorean theorem, area and volume equations, pi etc. Diagonal of a square is a√2 and area of a circle is πr². It just is. We can leave it as is or calculate an approximations.