Use the rule $\displaystyle\sqrt{{{a}{b}}}=\sqrt{{{a}}}\sqrt{{{b}}}\usepackage{cmbright}\Huge\$ and the definition of i.

$\displaystyle\sqrt{{-{200}}}=\sqrt{{{200}\cdot{\left(-{1}\right)}}}=\sqrt{{{200}}}\sqrt{{-{1}}}=\sqrt{{{100}}}\sqrt{{{2}}}\sqrt{{-{1}}}={10}\sqrt{{{2}}}{i}={10}{i}\sqrt{{{2}}}\usepackage{cmbright}\Huge\$