Prove that `3 + \sqrt{5}` is an irrational number.

Prove that 3+\sqrt{3} is an irrational number.

Show that 4 \sqrt{2} is an irrational number.

Show that 5\sqrt{3} is an irrational number.

prove that 5+sqrt(5) is an irrational numbers.

Show that 5+sqrt(7) is an irrational number.

Show that 4sqrt(2) I an irrational number.

Let r be relation from R (set of real numbers) to R defined by r={(a,b)|a, b in R and a-b+sqrt3 isan irrational number}. The relation r is