$\displaystyle{{7}}^{{2}}={49}\usepackage{cmbright}\Huge\$ , which is less than 52, and $\displaystyle{{8}}^{{2}}={64}\usepackage{cmbright}\Huge\$ , which is greater than52. The square root of 52 must be between 7 and 8, but there are no whole numbers between 7 and 8, so 52 is not a perfect square.