The value under the radical in a square root function cannot be less than 0. So the domain is all x-values for which the radicand is not negative. That means $\displaystyle{{x}}^{{2}}-{4}\ge{0}\usepackage{cmbright}\Huge\$ , so $\displaystyle{{x}}^{{2}}\ge{4}\usepackage{cmbright}\Huge\$ . This inequality is true only when x is greater than or equal to 2, or x is less than or equal to $\displaystyle-{2}\usepackage{cmbright}\Huge\$ : $\displaystyle{x}\ge{2}\usepackage{cmbright}\Huge\$ or $\displaystyle{x}\le-{2}\usepackage{cmbright}\Huge\$ .