Question

m and n are prime numbers then show√m+√n is an irrational number.

Answer 1

Step-by-step explanation

ASSUME THAT ROOTM AND ROOTN ARE RATIONAL

. Let √p + √q = a, where a is rational.

=> √q = a – √p Squaring on both sides

, we get q = a2 + p - 2a√p

=> √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.