Question

Prove
that
3+ √5 as irrational​

Answer 1

Answer:

Let us asume that 3+ √5 is rational ,

Where 3+ √5 =a\b

A and B are co prime numbers

3+ √5 =a\b

√5=a\b-3

√5=a-3b\b

a-3b\b is rational ..but we know that √5 is irrational

therefore our assumption is wrong

3+ √5 is irrational

Answer 2

let the 3+√5 is rational

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

√5 = a/b-3

√5 = a-3b/b

here we get that a-3b/b is rational no but we know the fact that √5 is irrational no

this arises from 3+√5

hence our assumption is wrong

hence 3+√5 is irrational no