Question

Prove that root 5 is an irrationtional number​

Answer 1

Answer:

let us assume √5 is rational.

√5=a/b,where a and b are coprimes or no other factor than 1.

a=√5b

squaring on both sides,

a²=(√5b)²

a²=5b² , a²is divisible by 5.

let a²=c²

c²=5b² , c²is divisible by 5.

So, a/b is rational and √5 is also rational. But this contradicts the fact that √5 is irrational and no common factor other than 1. This is because of our incorrect assumption.

hence, √5 is irrational..