Given the expression:
[tex]4\sqrt[]{-20}[/tex]To simplify the expression you have to use complex numbers.
Let "i" be equal to the square root of -1:
[tex]i=\sqrt[]{-1}[/tex]Then, you can rewrite the expression as follows:
[tex]\begin{gathered} 4\sqrt[]{20\cdot(-1)} \\ 4\sqrt[]{20}\cdot\sqrt[]{-1} \\ 4i\sqrt[]{20} \end{gathered}[/tex]Now that you have the square root of a positive number you can simplify it:
First, factor 20, you can write it as the product between 4 and 5:
[tex]4i\cdot\sqrt[]{4\cdot5}[/tex]Distribute the square root and simplify:
[tex]\begin{gathered} 4i\cdot\sqrt[]{4}\cdot\sqrt[]{5} \\ 4i\cdot2\cdot\sqrt[]{5} \\ (4\cdot2)i\sqrt[]{5} \\ 8i\sqrt[]{5} \end{gathered}[/tex]The simplified expression is:
[tex]8i\sqrt[]{5}[/tex]