Correct. 117 is between the perfect squares 100 and 121. So $\displaystyle\sqrt{{{117}}}\usepackage{cmbright}\Huge\$ must be between $\displaystyle\sqrt{{{100}}}\usepackage{cmbright}\Huge\$ and $\displaystyle\sqrt{{{121}}}\usepackage{cmbright}\Huge\$ .

$\displaystyle\sqrt{{{100}}}={10}\usepackage{cmbright}\Huge\$ and $\displaystyle\sqrt{{{121}}}={11}\usepackage{cmbright}\Huge\$

Because 117 is closer to 121 than it is to 100, $\displaystyle\sqrt{{{117}}}\usepackage{cmbright}\Huge\$ is probably about 10.8 or 10.9.

$\displaystyle{10.8}\cdot{10.8}={116.64}\usepackage{cmbright}\Huge\$ and $\displaystyle{10.9}\cdot{10.9}={118.81}\usepackage{cmbright}\Huge\$

$\displaystyle{{\left({10.8}\right)}}^{{2}}\usepackage{cmbright}\Huge\$ gives a closer approximation than $\displaystyle{{\left({10.9}\right)}}^{{2}}\usepackage{cmbright}\Huge\$ , so the answer is 10.8.