First find the principal square root of 63 and then find its opposite. To simplify the square root, factor 63 so that you have a perfect square times a number with no square factors:

$\displaystyle\sqrt{{63}}=\sqrt{{{9}\cdot{7}}}=\sqrt{{{3}\cdot{3}\cdot{7}}}=\sqrt{{{{3}}^{{2}}\cdot{7}}}\usepackage{cmbright}\Huge\$

Use $\displaystyle\sqrt{{{a}{b}}}=\sqrt{{a}}\cdot\sqrt{{b}}\usepackage{cmbright}\Huge\$ to rewrite the expression: $\displaystyle\sqrt{{{{3}}^{{2}}\cdot{7}}}=\sqrt{{{{3}}^{{2}}}}\cdot\sqrt{{7}}\usepackage{cmbright}\Huge\$

Take the square root of $\displaystyle{{3}}^{{2}}\usepackage{cmbright}\Huge\$ : $\displaystyle{3}\sqrt{{7}}\usepackage{cmbright}\Huge\$ .

The opposite of $\displaystyle{3}\sqrt{{{7}}}\usepackage{cmbright}\Huge\$ is $\displaystyle-{3}\sqrt{{{7}}}\usepackage{cmbright}\Huge\$ , so $\displaystyle-\sqrt{{{63}}}=-{3}\sqrt{{{7}}}\usepackage{cmbright}\Huge\$ .