Prove that `sqrtp+sqrtq` is an irrational, where p,q are primes.

Prove that sqrt2+sqrt2 is irrational .

Prove that number (log)_2 7 is an irrational number.

Prove that sqrt(3) is an irrational number. (Hint: Follow the method that we have used to prove sqrt(2) cancel(in) QQ .)

Prove that the following are irrational. sqrt5

Prove that the following are irrational. 6+sqrt2

Prove that the following are irrational. 1/sqrt2

Prove that q to p -= ~p to ~q

Prove that the following are irrational. 3+2sqrt5

Prove that the following are irrational. sqrt3 +sqrt5

For x >0,l e th(x)={1/q ,ifx=p/q0,ifxi si r r a t ion a l where p ,q >0 are relatively prime integers. Then prove that f(x) is continuous for all irrational values of xdot