Question

Reduce the square root of -360

Answer 1

reduce the square root of

`\begin{gathered} \sqrt[]{-360} \\ 360=36\cdot10=6^2\cdot10 \\ \end{gathered}`

There is no square root for the negative number

so, this is represent a complex number

So,

`\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}`