Question

Prove that 3 + 4√5 is an irrational number.

Answer 1

let the 3 + 4√5 be rational no

3 + 4√5 = a/b here a and b have no common factor

4√5 = a/b -3

4√5 = a-3b/b

√5 = a-3b/4b

we know the fact that√5 is irrational no

and now here we get a and b have common factor

this arises by assuming that 3+4√5 is rational

hence our assumption is wrong

hence 3+4√5 is irrational no.