Prove that root 5is irrational

Let √5 be rational such that √5=p/q where p nd q are co prime numbers. Now;√5=p/q. q√5=p . Squaring both sides; 5q^2=p^2. .......(1) also;p =5s for some integer s;putting p=5s in (1) 5q^2=(5s)^2. 5q^2=25s^2. From (1) nd(2) weconclude that 5is a common factor of p^2as well as p nd q^2as well as q.Hence;our assumption that p nd q are co prime integers is wrong.therefore √5is irrational by contradiction. Hope it will help u.