Question

Prove that √p+√q is irrational, where p, qare primes. How

Answer 1

Answer:

Step-by-step explanation:

Let us suppose that √p + √q is rational.

Let √p + √q = a, where a is rational.

=> √q = a – √p

Squaring on both sides, we get

q = a² + p - 2a√p

=> $\sqrt{p} =\frac{(a^{2} +p-q)}{2a}$, which is a contradiction as the right hand side is rational number, while √p is irrational.

Hence, √p + √q is irrational.