Question

Prove that √p + √r are Irrational numbers where p,q are Prime Numbers.

Chapter: Real Numbers
Class: Tenth
[Will mark Brainliest if I get my Answer in Less than 30 Minutes!]​

Answer 1

Answer:

= √p + √q = a/b

∴ By Squaring on Both sides,

= (√p + √q)² = (a/b)²

= (√p)² + (√q)² + 2√pq = a²b²

= p + q + 2√pq = a²/b²

= p + q + 2√pq = a²/b²

= a²b² - p - q = 2√pq

∵ LHS ≠ RHS

∴ p, q are Prime Numbers

Hence, pur Assumption that √p+√q is a Rational Number is False (or)  Wrong.

∴ √p+√q is Irrational.