Question

Simplify. Leave answer in a+bi form:4√(-20)

Answer 1

Given the expression:

`4\sqrt[]{-20}`

To simplify the expression you have to use complex numbers.

Let "i" be equal to the square root of -1:

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

Then, you can rewrite the expression as follows:

`\begin{gathered} 4\sqrt[]{20\cdot(-1)} \\ 4\sqrt[]{20}\cdot\sqrt[]{-1} \\ 4i\sqrt[]{20} \end{gathered}`

Now that you have the square root of a positive number you can simplify it:

First, factor 20, you can write it as the product between 4 and 5:

`4i\cdot\sqrt[]{4\cdot5}`

Distribute the square root and simplify:

`\begin{gathered} 4i\cdot\sqrt[]{4}\cdot\sqrt[]{5} \\ 4i\cdot2\cdot\sqrt[]{5} \\ (4\cdot2)i\sqrt[]{5} \\ 8i\sqrt[]{5} \end{gathered}`

The simplified expression is:

`8i\sqrt[]{5}`