Answer: [tex]2i\sqrt{3}[/tex]
where [tex]i = \sqrt{-1}[/tex]
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Work Shown:
[tex]x = \sqrt{-12}\\\\x = \sqrt{-1*4*3}\\\\x = \sqrt{-1}*\sqrt{4}*\sqrt{3}\\\\x = i*2*\sqrt{3}\\\\x = 2i\sqrt{3}\\\\[/tex]
Therefore, [tex]\sqrt{-12} = 2i\sqrt{3}[/tex]
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Explanation:
The basic steps are to factor the radicand such that we pull out the -1 and we also pull out the largest perfect square factor. That way we can then apply the rule [tex]\sqrt{A*B} = \sqrt{A}*\sqrt{B}[/tex] to break up the root and simplify.
