Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals. $-\sqrt{-84}$

Explanation:

Step1: Rewrite negative radicand

$-\sqrt{-84} = -\sqrt{84 \times (-1)}$

Step2: Separate radicals

$= -\sqrt{84} \times \sqrt{-1}$

Step3: Simplify $\sqrt{84}$ and substitute $i=\sqrt{-1}$

$\sqrt{84} = \sqrt{4 \times 21} = 2\sqrt{21}$, so:
$= -2\sqrt{21}i$

Answer:

$-2\sqrt{21}i$