use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals…

Explanation:

Step1: Separate the negative sign

$$\sqrt{-92}=\sqrt{-1\times92}$$

Step2: Use the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$

$$\sqrt{-1\times92}=\sqrt{-1}\times\sqrt{92}$$ Since $\sqrt{-1}=i$, the expression becomes $i\sqrt{92}$.

Step3: Simplify the radical $\sqrt{92}$

Factorize 92: $92 = 4\times23$. Then $\sqrt{92}=\sqrt{4\times23}$. Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ again, $\sqrt{4\times23}=\sqrt{4}\times\sqrt{23}=2\sqrt{23}$.

Answer:

$2i\sqrt{23}$