Question

Prove that √5 is an irrational number and hence show that 2 - √5 is also an irrational number.

Answer 1

Let √5  be a rational number.

√5 = a / b ,

(a, b are co-primes and b  ≠ 0)

or,                     a =  b√5

On squaring both the sides, we get

 

    or,              2- a = √5 

2 - a is rational

But √5 is not rational

:. 2 - √5  is irrational.