If one thinks about it, one will realize that there are some fractions which are really close to the square root of 2. Rational numbers are numbers that can be expressed as a fraction. Irrationals are the opposite. They are numbers that are not fractions. Why is the square root of 2 irrational? First, one should compare the square root of 2 to a number very close to it. More specifically, 665 857/470 832, which is off by 10-12. There are definitely better estimates. For example, 4 946 041 176 255 201 878 775 086 487 573 351 061 418 968 498 177/3 497 379 255 757 941 172 020 851 852 070 562 919 437 964 212 608 is a very good estimate, but this is not going to be used because I don’t want to type 4 946 041 176 255 201 878 775 086 487 573 351 061 418 968 498 177/3 497 379 255 757 941 172 020 851 852 070 562 919 437 964 212 608 every single time I want to mention it because it is soooooooooooooooooooooo long. Too long, as most people would say. Another example is 17/12, which one can be used for most purposes because you do not need a very accurate number, but not this one because this requires preciseness, so a number in the middle was chosen. If root 2 (the square root of 2) is equal to 665 857/470 832 or anything mentioned before, then it is rational, because every fraction is rational. If root 2 is rational, then it would have decimals that repeat, and there is no evidence of that, and that is why root 2 is irrational! That is also why all other fractions will not work too. Also, all other square roots are irrational for the same reason, except for the square roots of ‘perfect’ squares. They are called perfect squares because when one takes the square root of them, you get a rational number. A funny story is that I got this information by bugging my parents. Who knew that you can get so much information like that?
