Question

prove that root of p+root of q is irrational where p,q are primes

Answer 1

Let √p+√q is rational number
A rational number can be written in the form of a/b√p+√q=a/b√p=a/b-√q√p=(a-b√q)/bp, q are integers then (a-b√q) /b is a rational number.
So, √p is also a rational number.
But this contradicts the fact that √p is an irrational number.so, our supposition is false√p+√q is an irrational number.