let us assume that √7 be rational.then it must in the form of p / q.As definition of rational number says.. P is whole number q is non zero whole number.. And p and q is simplest ratio which is expressed.. That means there exists no prime factor common in p and q.√7 = p / q√7 x q = psquaring on both sides7q² = p² ——1.p is divisible by 7p = 7c [c is a positive integer] [squaring on both sides ]p²= 49c²subsitute p² in eqn(1) we get7q² = 49 c²q² = 7c²q is divisble by 7thus q and p have a common factor 7.there is a contradiction to our assumptionas our assumsion p & q are co prime but it has a common factor.so that √7 is an irrational.