Question

Prove that $\sqrt{p}+ \sqrt{q}$ is an irrational number given that p and q are primes.

Answer 1

√p +√q is a rational 
√p +√q =a where a is a rational number
√q=a-√p
squaring both sides
q=a^2+p-2√pa
2√pa=a^2+p-q
√p=a^2+p-q/2a

which is a contradiction as right hand side is rational but left hand side is irrationa;

Answer 2

Heya....

====== Answer =======

√p + √q is natural no

√p+√q = a , a is rational no

√q = a-√p

Squaring both the sides ,,

q = q^2+p-2√pa

2√pa = q^2 + pq

In this, there is a contradiction , left side is rational,,

And....

Right side is irrational ....

Thank you