Question

2. Prove that Vp +Tq is irrational, where
P, q are primes.​

Answer 1

Answer:

Solution:Let us suppose that √p + √q is rational.Let √p + √q = a where a is rational.=> √q = a – √pSquaring on both sides we getq = a2 + p - 2a√p=> √p = a2 + p - q/2a which is a contradiction as the right hand side is rational number while √p is irrational.Hence √p + √q is irrational.