If `p ,\ q` are prime positive integers, prove that `sqrt(p)+sqrt(q)` is an irrational number.

Prove that sqrt(p)+sqrt(q) is an irrational,where p and q are primes.

Prove that for any prime positive integer p,quad sqrt(p) is an irrational number.

If p and q are positive integers, then (p)/(q) is a ______ rational number and (p) (-q) is a ______ rational number.

If p and q are primes such that p=q+2 prove that p^(p)+q^(q) is a multiple of p+q

If p and q are positive integers, then which one of the following equations has p-sqrt(q) as one of its roots ?

If r,s,t are prime numbers and p,q are the positive integers such that LCM of p,q is r^(2)s^(4)t^(2) , then the number of ordered pairs (p,q) is:

If p,q and r ( pneq ) are terms ( not necessarily consecutive) of an A.P., then prove that there exists a rational number k such that (r-q)/(q-p) =k. hence, prove that the numbers sqrt2,sqrt3 and sqrt5 cannot be the terms of a single A.P. with non-zero common difference.

Assertion : sqrt2 is an irrational number. Reason : If p be a prime, then sqrtp is an irrational number.