Question

prove that
under root p +under root q
are irrational number where p and q are prime number​

Answer 1

Now x, x², p, q and 2 are all rational, and rational numbers are closed under subtraction and division. So (x² - p - q) / 2 is rational. But since p and q are both primes, then pq is not a perfect square and therefore √(pq) is not rational.