Root 7 is irrational

1.	Root 7 is irrational
Answer» Yogita Ingle\xa01\xa0year, 7\xa0months agolet us assume that √7 be rational.then it must in the form of p / q [q ≠ 0] [p and q are co-prime]√7 = p / q=> √7 x q = psquaring on both sides=> 7q2= p2 ------ (1)p2\xa0is divisible by 7p is divisible by 7p = 7c [c is a positive integer] [squaring on both sides ]p2\xa0= 49 c2\xa0--------- (2)Subsitute p2\xa0in equ (1) we get7q2\xa0= 49 c2q2\xa0= 7c2=> q is divisible by 7thus q and p have a common factor 7.there is a contradictionas our assumsion p & q are co prime but it has a common factor.So that √7 is an irrational.

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