Question

prove that
$\sqrt{p} + \sqrt{q}$
is an irrational,where p and q are prime

Answer 1

let assume, √p+√q =a/b
Squaring both sides
(√p+√q)²=(a/b)²
p+q+2√pq=(a/b)²
√pq=1/2{(a/b)²-p-q}
Now p and q are prime positive numbers so that √p and √q are irrational
irrational=rational
So contradiction.

Hope it will help you...