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

User Mfe
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1 Answer

18 votes
18 votes

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}

User Andybalholm
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