Question

Find the cube root of -8:3sqrt-8

Answer 1

To find the cube root of \(-8\), we want to find a number \(x\) such that \(x^3 = -8\).

The cube root of \(-8\) is calculated as follows:

\[
\sqrt[3]{-8} = -2
\]

This is because \((-2) \times (-2) \times (-2) = -8\).

Now, you also mentioned \(3\sqrt{-8}\).

First, let's evaluate \(\sqrt{-8}\):

\[
\sqrt{-8} = \sqrt{8} \cdot \sqrt{-1} = \sqrt{8}i = 2\sqrt{2}i
\]

Now, multiplying this by \(3\):

\[
3\sqrt{-8} = 3 \cdot 2\sqrt{2}i = 6\sqrt{2}i
\]

In summary:

- The cube root of \(-8\) is \(-2\).
- The expression \(3\sqrt{-8}\) evaluates to \(6\sqrt{2}i\).