reduce the square root of
[tex]\begin{gathered} \sqrt[]{-360} \\ 360=36\cdot10=6^2\cdot10 \\ \end{gathered}[/tex]There is no square root for the negative number
so, this is represent a complex number
So,
[tex]\begin{gathered} \sqrt[]{-360}=\sqrt[]{-1}\cdot\sqrt[]{360} \\ =i\cdot\sqrt[]{6^2\cdot10} \\ =i\cdot6\sqrt[]{10} \\ =6\sqrt[]{10}\cdot i \end{gathered}[/tex]