Question

Simplify

Answer 1

Answer: $4\sqrt{3}$

Step-by-step explanation:

For this exercise it is important to remember the following:

$i=\sqrt{-1} \\\\i^2=-1$

Given the following expression:

$-2i\sqrt{-12}$

You can notice that the radicand (the number inside the square root) is negative. Therefore, in order to simplify the expression, you need to follow these steps:

1. Replace $\sqrt{-1}$ with $i$ and simplify:

$(-2i)(i)\sqrt{12}=-2i^2\sqrt{12}=-2(-1)\sqrt{12}=2\sqrt{12}$

2. Descompose 12 into its prime factors:

$12=2*2*3=2^2*3$

3. Substitute into the expression:

$=2\sqrt{2^2*3}$

4. Since $\sqrt[n]{a^n}=a$, you can simplify it:

$=(2)(2)\sqrt{3}=4\sqrt{3}$