$\displaystyle{{12}}^{{2}}={144}\usepackage{cmbright}\Huge\$ , which is less than 164, and $\displaystyle{{13}}^{{2}}={169}\usepackage{cmbright}\Huge\$ , which is greater than 164. The square root of 164 must be between 12 and 13, but there are no whole numbers between 12 and 13, so 164 is not a perfect square.