Question

Prove that root p + root q is an irrational, where p, q are primes​

Answer 1

Answer:

Answer Expert Verified

Rational numbers are closed under multiplication, so if we square both sides, we still get rational numbers on both sides. ... 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.

Answer 2

Step-by-step explanation:

Rational numbers are closed under multiplication, so if we square both sides, we still get rational numbers on both sides. ... 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