Question

If m and n are prime positive integers,prove that (√m+√n) is an irrational number

Answer 1

Solution:

It is given that , m and n are prime positive integers.

it means , prime factors of m , are 1 and m ,and Prime factors of n are 1 and n respectively.

As, every square root of prime number is an irrational number.

For example, if 2 and 3 are prime numbers , then $\sqrt{2} and \sqrt{3}$ are irrational numbers.

As, sum of two irrational number is an irrational number.

→→So we can say that, if m and n are Prime positive integers, then  $\sqrt{m} + \sqrt{n}$  is an irrational number.