Where are some places you can find irrational numbers?

Answer 1

Almost anywhere in geometry.

If a circle has an rational radius, its circumference and area will be irrational. Conversely, if the area is rational then the radius will be irrational.

The ratio of the diagonal of a square to its side is always sqrt(2) - an irrational. So if the sides are of rational length then the diagonal is irrational.

There are lots of other common objects where the fact that some of the measures are rational forces other measures to be irrational.

And circles and squares are all around you. Your glass / coffee mug is probably circular. Your plates, bowls etc.

The ratio of the length to width of standard paper (A4) is irrational.