First find the principal square root of 72 and then find its opposite. To simplify the square root, factor 72 so that you have a perfect square times a number with no square factors:

$\displaystyle\sqrt{{72}}=\sqrt{{{36}\cdot{2}}}=\sqrt{{{6}\cdot{6}\cdot{2}}}=\sqrt{{{{6}}^{{2}}\cdot{2}}}\usepackage{cmbright}\Huge\$

Use $\displaystyle\sqrt{{{a}{b}}}=\sqrt{{a}}\cdot\sqrt{{b}}\usepackage{cmbright}\Huge\$ to rewrite the expression: $\displaystyle\sqrt{{{{6}}^{{2}}\cdot{2}}}=\sqrt{{{{6}}^{{2}}}}\cdot\sqrt{{{2}}}\usepackage{cmbright}\Huge\$ .

Take the square root of $\displaystyle{{6}}^{{2}}\usepackage{cmbright}\Huge\$ : $\displaystyle{6}\sqrt{{{2}}}\usepackage{cmbright}\Huge\$ .

The opposite of $\displaystyle{6}\sqrt{{{2}}}\usepackage{cmbright}\Huge\$ is $\displaystyle-{6}\sqrt{{{2}}}\usepackage{cmbright}\Huge\$ , so $\displaystyle-\sqrt{{{72}}}=-{6}\sqrt{{{2}}}\usepackage{cmbright}\Huge\$ .