Question

Write √(-12) in simplest radical form

Answer 1

Answer:  $2i\sqrt{3}$

where $i = \sqrt{-1}$

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Work Shown:

$x = \sqrt{-12}\\\\x = \sqrt{-1*4*3}\\\\x = \sqrt{-1}*\sqrt{4}*\sqrt{3}\\\\x = i*2*\sqrt{3}\\\\x = 2i\sqrt{3}$

Therefore, $\sqrt{-12} = 2i\sqrt{3}$

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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 $\sqrt{A*B} = \sqrt{A}*\sqrt{B}$ to break up the root and simplify.