Question:
Prove that $(2+\sqrt{3})$ is irrational.
Solution:
Let $(2+\sqrt{3})$ be rational.
Then, both $(2+\sqrt{3})$ and 2 are rational.
$\therefore\{(2+\sqrt{3})-2\}$ is rational [ $\because$ Difference of two rational is rational]
$\Rightarrow \sqrt{3}$ is rational.
This contradicts the fact that $\sqrt{3}$ is irrational.
The contradiction arises by assuming $(2+\sqrt{3})$ is rational.
Hence, $(2+\sqrt{3})$ is irrational.