Question

Move numbers to the blanks to rewrite each square root.
`√( - 4) =`
`√( - 5 = )`answers:
`2i`
`- 2`
`4i`
`√(5i)`
`- √(5)`
`i √(5)`

Answer 1

We have 2 expressions:

`\begin{gathered} a)\text{ }\sqrt[]{-4} \\ b)\sqrt[]{-5} \end{gathered}`

Case a.

We can rewrite our square root as

`\sqrt[]{-4}=\sqrt[]{-1*4}=\sqrt[]{-1}*\sqrt[]{4}`

but by definition

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

which is the imaginary number. So, our square root is equal to

`\sqrt[]{-4}=\sqrt[]{4}i`

which corresponds to option 3.

Case b.

Similarly,

`\sqrt[]{-5}=\sqrt[]{-1}*\sqrt[]{5}`

and the answer is

`\sqrt[]{-5}=i\sqrt[]{5}`

which corresponds to option 6