We have the following number, we need to simplify:
[tex]6\cdot\sqrt[]{-2401}[/tex]
we can also express this as:
[tex]\begin{gathered} 6\cdot\sqrt[]{(-1)\cdot(2401)} \\ 6\sqrt[]{(-1)\cdot(49)\cdot(49)} \end{gathered}[/tex][tex]\begin{gathered} =6\sqrt[]{-1\cdot49^2} \\ =6\cdot\sqrt[]{-1}\cdot\sqrt[]{49^2} \\ =6\cdot\sqrt[]{-1}\cdot49 \\ =6\cdot49\cdot\sqrt[]{-1} \end{gathered}[/tex]
since:
[tex]\sqrt[]{-1}=i[/tex]
which represents the imaginary number,
then, we get:
[tex]6\sqrt[]{-2401}=6\cdot49\cdot i=294i[/tex]
