Question 1001489
I just posted one possibility...

Prove {{{sqrt(x + (1/x))}}} is irrational.
If the radicand is not a perfect square, then the root must be irrational.
We can rewrite the radicand as
x + 1/x = (x+1)/x
The only way (x+1)/x can be a perfect square is if x+1 and x are both perfect squares...
If x is a perfect square, then x+1 cannot be.
If x+1 is a perfect square, then x cannot be.
Thus {{{sqrt(x + (1/x))}}} is irrational.