Question

Express the radical using the Imaginary unit, i.Express your answer in simplified form.#v-20 = +

Answer 1

`\text{the answer in the box = }2i\sqrt[]{5}`Step-by-step explanation:
`\pm\sqrt[]{-20}`

Using imaginary unit i:

Recall i² = -1

-20 = -1 × 20 = i² × 20

`\begin{gathered} \pm\sqrt[]{-20}\text{ = }\pm\sqrt[]{i^(2)*20} \\ \sqrt[]{20}\text{ = }\sqrt[]{4*5}\text{ = 2}\sqrt[]{5} \end{gathered}`
`\begin{gathered} \pm\sqrt[]{i^2*20}\text{ = }\pm\sqrt[]{i^2}*\sqrt[]{20} \\ =\pm(i*2\sqrt[]{5)}\text{ = }\pm2i\sqrt[]{5} \\ \text{the answer in the box = }2i\sqrt[]{5} \end{gathered}`