[tex]\text{the answer in the box = }2i\sqrt[]{5}[/tex]
Explanation:[tex]\pm\sqrt[]{-20}[/tex]
Using imaginary unit i:
Recall i² = -1
-20 = -1 × 20 = i² × 20
[tex]\begin{gathered} \pm\sqrt[]{-20}\text{ = }\pm\sqrt[]{i^{2}\times20} \\ \sqrt[]{20}\text{ = }\sqrt[]{4\times5}\text{ = 2}\sqrt[]{5} \end{gathered}[/tex][tex]\begin{gathered} \pm\sqrt[]{i^2\times20}\text{ = }\pm\sqrt[]{i^2}\times\sqrt[]{20} \\ =\pm(i\times2\sqrt[]{5)}\text{ = }\pm2i\sqrt[]{5} \\ \text{the answer in the box = }2i\sqrt[]{5} \end{gathered}[/tex]
