Question

Prove that root p plus root q is irrational..

With correct steps!!

Answer 1

Answer:

√p & √q are irrational, so √pq is also irrational

Let √p + √q be rational = a/b , where a and b are co-prime integers.

√p + √q = a/b

(√p + √q)² = a²/b²

p + q + 2√pq = a²/b²

√pq = a²/b² - p - q

But a²/b² - p - q is rational, whereas √pq is irrational. So our assumption was wrong.

Therefore, √p + √q is irrational.