" prove that "sqrt(11)" is isrational mumben "

Prove that sqrt(11) is irrational.

Prove that sqrt(11) is irrational.

Prove that sqrt5+sqrt11 is irrational.

Prove that sqrt2+sqrt11 is an irrational number.

Prove that (2sqrt7)/(sqrt11) is irrational.

prove that sqrt108 -sqrt75=sqrt3

Prove that sqrt i+sqrt(-i)=sqrt 2

Prove by the method of contradiction, " P:sqrt11 is irrational."

Let f(x)=("lim")_(mvecoo){("lim")_(nvecoo)cos^(2m)(n !pix)}, where x in Rdot Then prove that f(x)={1,if x isrational 0,if x is irrational