$\displaystyle\sqrt{{3}}\usepackage{cmbright}\Huge\$ must be between $\displaystyle\sqrt{{1}}\usepackage{cmbright}\Huge\$ and $\displaystyle\sqrt{{4}}\usepackage{cmbright}\Huge\$ . Since $\displaystyle\sqrt{{1}}={1}\usepackage{cmbright}\Huge\$ and $\displaystyle\sqrt{{4}}={2}\usepackage{cmbright}\Huge\$ , the number $\displaystyle\sqrt{{{3}}}\usepackage{cmbright}\Huge\$ is between 1 and 2. This tells you that it is not a whole number. However, since 3 is not a perfect square, $\displaystyle\sqrt{{3}}\usepackage{cmbright}\Huge\$ is irrational.