Question

show that root p+root q is an irrational number where p and q are prime ​

Answer 1

Let √p + √q = a, where a is rational. => √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. Rational numbers are closed under multiplication, so if we square both sides, we still get rational numbers on both sides.

Answer 2

Step-by-step explanation:

here it's given that p and q are prime number also we know that their are no factors of prime number except 1 so we able to say that root p+ root q is an irrational number