Question

Reduce the square root of -8

Answer 1

We have to simplify:

`\sqrt[]{-8}`

We first use the radical property shown below to write it as:

Radical Property:

`\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}`

Thus, we can write this problem as:

`\sqrt[]{-8}=\sqrt[]{(-1)(8)}=\sqrt[]{-1}\sqrt[]{8}`

We know the square root of -1 is i, thus we may write:

`\sqrt[]{8}i`

Now we can again use the radical property to break apart root 8. Shown below:

`\begin{gathered} \sqrt[]{8}i \\ =\sqrt[]{2*2*2}i \\ =\sqrt[]{2}\sqrt[]{2}\sqrt[]{2}i \end{gathered}`

Now we can further simply using

`\sqrt[]{x}\sqrt[]{x}=x`

Thus, the final simplification would be:

`\sqrt[]{-8=}2\sqrt[]{2}i`