How to prove that √5 is irrational?

1.	How to prove that √5 is irrational?
Answer» let root 5 be rationalthen it must in the form of p/q [q is not equal to 0][p and q are co-prime]root 5=p/q=> root 5 × q = psquaring on both sides=> 5×q×q = p×p ------> 1p×p is divisible by 5p is divisible by 5p = 5c [c is a positive integer] [squaring on both sides ]p×p = 25c×c --------- > 2sub p×p in 15×q×q = 25×c×cq×q = 5×c×c=> q is divisble by 5thus q and p have a common factor 5there is a contradictionas our assumsion p &q are co prime but it has a common factorso\xa0√5 is an irrational How to prove underroot 5 is irrational

Discussion