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:

$\begin{gathered} \sqrt[]{8}i \\ =\sqrt[]{2\times2\times2}i \\ =\sqrt[]{2}\sqrt[]{2}\sqrt[]{2}i \end{gathered}$

Now we can further simply using

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

Thus, the final simplification would be:

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