Answer: [tex]4\sqrt{3}[/tex]
Step-by-step explanation:
For this exercise it is important to remember the following:
[tex]i=\sqrt{-1} \\\\i^2=-1[/tex]
Given the following expression:
[tex]-2i\sqrt{-12}[/tex]
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 [tex]\sqrt{-1}[/tex] with [tex]i[/tex] and simplify:
[tex](-2i)(i)\sqrt{12}=-2i^2\sqrt{12}=-2(-1)\sqrt{12}=2\sqrt{12}[/tex]
2. Descompose 12 into its prime factors:
[tex]12=2*2*3=2^2*3[/tex]
3. Substitute into the expression:
[tex]=2\sqrt{2^2*3}[/tex]
4. Since [tex]\sqrt[n]{a^n}=a[/tex], you can simplify it:
[tex]=(2)(2)\sqrt{3}=4\sqrt{3}[/tex]
