${\displaystyle \frac{3}{\mathrm{\surd }5}}$
Let asuume that $\frac{3}{\sqrt{5}}$ is rartional
$\frac{3}{\sqrt{5}},\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{3\sqrt{5}}{5}$
where $\frac{3\sqrt{5}}{5}$ is rational.
which shows that $\frac{3}{5}$ is rational and $\surd 5$ is rational
but the fact is $\mathrm{\surd }5$ is an irrational.
our assumption is wrong, and
$\frac{3}{\sqrt{5}}$is irrational.