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}}>-{4}\usepackage{cmbright}\Huge\$ . This inequality is always true because any real number squared will result in a positive number or 0. So the domain is all real numbers.