Question

prove that 3 plus 2 root 5 is an irrational number

Answer 1

Let 3+2√5 be a rational number

3+2√5=p/q. (where p,q are co primes)

2√5=(p/q)-3

√5=[(p/q)-3]/2

As p,q,3 and 2 are rationals

RHS is a rational number

As RHS is a rational that implies LHS i.e.,√5 is a rational number

This is a contradiction to the fact that √5 is an irrational number

therefore, our assumption is wrong

therefore 3+2√5 is an irrational number

Hence proved