\((2-3 \sqrt{5})\)

Let us assume that \((2-3 \sqrt{5})\) is rational.

subtract given numbers from 2 , considering 2 is rational number. as we know, difference of two rational numbers is rational

\(2-(2-3 \sqrt{5})\) is rational.

\(\Rightarrow 3 \sqrt{5}\) is rational

above result is possible if 3 is rational and \(\sqrt{5}\) is rational. Because, product of two rational numbers is rational.

but the fact is \(\sqrt{5}\) is an irrational.

Our assumption is wrong, and \((2-3 \sqrt{5})\) is irrational