Question

Show that $2-\sqrt{3}$ is an irrational number.

Answer 1

Let us assume that is rational .Then, there exist positive co primes a and b such that
$$\begin{gathered} 2-\sqrt{3}=\frac{a}{b} \\ \sqrt{3}=2-\frac{a}{b} \end{gathered}$$
This implies, $\sqrt{3}$ is a rational number, which is a contradiction.
Hence, is irrational number.