Show that ` (2+sqrt3)` is a irrational number.

Explanation

let us assume to the contrary , that ` ( 2 + sqrt3)` is rational.
Then , there exist co-primnes a and b (` b ne 0`) such that
` (2 +sqrt3) = a/b` ltbr. ` Rightarrow sqrt3 = a/b -2 Rightarrow sqrt3 = ( a-2b)/b`
Since a and b are integers , so `(a -2b)/b` is rational .
Thus, ` sqrt3` is also rational.
But, this contradicts that fact that ` sqrt3` is irrational , so, our asumption is incorrect.
Hence ( ` 2 sqrt3)` is irrational. \