Question

Prove that root2+root5 is irrational

Answer 1

Let's assume that √2+√5 is a rational number.

Therefore it can be represented as

m/p=√2+√5 (where m,p are integers with gcd 1)

m/p=√2+√5/1

Therefore m=√2+√5 & p=1

But √2+√5 is not an integer which contradicts our assumption.

Hence √2+√5 is an irrational number.