Sorry for any mispellings, English is not my first language. So, I'm studying irrational numbers and I got curious about something and my teacher couldn't give me the answer. I understand Pi must exist because it's the simple result of a division (perimeter by diameter). But how can the mathematicians say there is the square root of 2? If there is no number that we can write down to a piece of paper and then multiply this number by itself and obtain 2 as a result, then there is no square root of 2, in my opinion. Is the square root of 2 like something made up to make mathematics work? (like factorial of 0)? Thank you.