Question

Prove 3÷2root 5 be rational

Answer 1

Let us assume to the contrary that 3/2 √5 is rational. then we can find coprimes a and b such that 3/2 √5=a/b,where b≠0.

3/2 √5=a/b

√5=a*2/b*3

since a,b,2 and 3 are integers,√5 is rational. but this contradicts the fact that √5 is irrational. this contradiction has arisen because of our incorrect assumption that 3/2 √5 is rational. so 3/2√5 is irrational.