Question

Why cant contradiction method be used to prove irrationality of square root of any number?
Think about it this way, if the number whose irrationality is being proved is $\sqrt{p}$(follow the attached image for reference), what is stopping it from being proved irrational? In this manner i can prove any and every number irrational. Pls help.

Answer 1

Answer:

See, when you prove irrationality, you always assume the √p to be rational. But when you get the answer, it contradicts your assumption that √p is rational. There is no other way to prove irrationality of a number except the CONTRADICTION METHOD

Refer the attachment. You will have an idea about it.

Good Question though. Keep it up.

Answer 2

see the above attachment