Here’s a question: is the square root of 2 only an irrational number because we’re using base 10? For example, 10/3 is a non-terminating decimal: 3.333… Consider that in base 3, 10/3 is a terminating “decimal.” That is, 101(base 3) / 10 (base 3) = 1.1 (base 3). It terminates. Is there a base numbering system in which the square root of 2 is a rational number?

This question has bothered me for a long time, and I don’t know how to solve it.