First find the principal square root of 96 and then find its opposite. To simplify the square root, factor 96 so that you have a perfect square times a number with no square factors:

$\displaystyle\sqrt{{96}}=\sqrt{{{16}\cdot{6}}}=\sqrt{{{4}\cdot{4}\cdot{6}}}=\sqrt{{{{4}}^{{2}}\cdot{6}}}\usepackage{cmbright}\Huge\$

Use $\displaystyle\sqrt{{{a}{b}}}=\sqrt{{a}}\cdot\sqrt{{b}}\usepackage{cmbright}\Huge\$ to rewrite the expression: $\displaystyle\sqrt{{{{4}}^{{2}}\cdot{6}}}=\sqrt{{{{4}}^{{2}}}}\cdot\sqrt{{6}}\usepackage{cmbright}\Huge\$

Take the square root of $\displaystyle{{4}}^{{2}}\usepackage{cmbright}\Huge\$ : $\displaystyle{4}\sqrt{{{6}}}\usepackage{cmbright}\Huge\$

The opposite of $\displaystyle{4}\sqrt{{6}}\usepackage{cmbright}\Huge\$ is $\displaystyle-{4}\sqrt{{{6}}}\usepackage{cmbright}\Huge\$ , so $\displaystyle-\sqrt{{{96}}}=-{4}\sqrt{{{6}}}\usepackage{cmbright}\Huge\$ .