Question

let p and q are positive prime numbes ,then prove that √p+√q is an irrational number

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

=> √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.

Answer 2

Answer:

proof is already Nicely enclosed by other Teacher , who should get Brainiiest. BUT anyhow , remember prime numbers DO NOT have rational Roots ans sum of Irrational is Irrational .