$\displaystyle{{4}}^{{2}}={16}\usepackage{cmbright}\Huge\$ , which is less than 20, and $\displaystyle{{5}}^{{2}}={25}\usepackage{cmbright}\Huge\$ , which is greater than 20. The square root of 20 must be between 4 and 5, but there are no whole numbers between 4 and 5, so 20 is not a perfect square.