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Let us assume that √5 is a rational number. we know that the rational numbers are in the form of p/q form where p,q are intezers. so, √5 = p/q p = √5q we know that 'p' is a rational number. so √5 q must be rational since it equals to p but it doesnt occurs with √5 since its not an intezer therefore, p =/= √5q this contradicts the fact that √5 is an irrational number hence our assumption is wrong and √5 is an irrational number.

Assume that √5 is irrational such that √5= a/b where a and b are co prime b=√5a b²=5a² so ,5 divides b b=5c b²=25c² 5a²=25c² a²=5c² so , 5 divides a this contadicts the fact that a and b are co prime so √5 is irrational