How is the irrationality of the square root of 2 important in the 21st century?

Question

Are there any practical applications of the square root of 2 in careers or in daily life? If so, how does it affect you?

Answer 1

If mathematicians were to some day discover that there is no difference between rational and irrational numbers, it wouldn't make much of an immediate difference in ordinary everyday life. However, especially now that symbolic mathematical computation (not numerical computation) is expanding in use, the existence of rational numbers as distinct from irrationals can have a profound impact on exact mathematical expression. And since so much of technology and engineering is becoming increasingly dependent on on such symbolic mathematical computation, the existence of irrational numbers can have an indirect inluence on the "practical 21st century applications".

I should maybe elaborate this and say that just like there are certain numbers that cannot be expressed as a rational fractions, there are polynomial equations which roots cannot be expressed with a finite expression. Likewise, there are certain integrals that have no finite explicit expression, nor there are such solutions to certain differential equations, etc. There is a deep connection between number theory and symbolic mathematics, which is why questions on the irrationality of the square root of 2 is far from trivial or unimportant.