Question

Rewrite Each square root.√-4 = ?√-5 = ?

Answer 1

Given the expressions:

`\begin{gathered} \sqrt[]{-4} \\ \sqrt[]{-5} \end{gathered}`

remember that we can factor the -1 and use the following property of imaginary numbers:

`\sqrt[]{-1}=i`

then, we have the following:

`\begin{gathered} \sqrt[]{-4}=\sqrt[]{-1\cdot4}=\sqrt[]{-1}\cdot\sqrt[]{4}=2\cdot i \\ \sqrt[]{-5}=\sqrt[]{-1\cdot5}=\sqrt[]{-1}\cdot\sqrt[]{5}=\sqrt[]{5}\cdot i \end{gathered}`