Prove root5 is irrational no.

1.	Prove root5 is irrational no.
Answer» let √5 be rationalthen it must in the form of p/q [q is not equal to 0][p and q are co-prime]√5=p/q⇒ √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 = 25× c× 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

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