$$ =\quad $$ Question 26 of 28 (1 point) | Question Attempt: 1 of 1 $$

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$$ =\quad $$ Question 26 of 28 (1 point) | Question Attempt: 1 of 1 $$ <=16 \quad \equiv 17 \quad \equiv 19 \quad \equiv 20 \quad \equiv 21 \quad \equiv 22 \quad \equiv 23 $$ Write in terms of $$ i $$. Simplify your answer as much as possible. $$ -\sqrt{-80} $$

UpStudy AI · Accepted Answer

Step 1: Rewrite the expression $$-\sqrt{-80}$$ as $$-\sqrt{80} \cdot \sqrt{-1}$$.

Step 2: Recognize that $$\sqrt{-1} = i$$, so the expression becomes $$-\sqrt{80} \cdot i$$.

Step 3: Simplify $$\sqrt{80}$$. Since $$80 = 16 \cdot 5$$, we have $$\sqrt{80} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5}$$.

Step 4: Substitute back into the expression: $$-\sqrt{-80} = -4\sqrt{5} \cdot i$$.

Step 5: The final simplified form is $$8i$$.8i

\( =\quad \) Question 26 of 28 (1 point) | Question Attempt: 1 of 1 \[ <=16 \quad \equiv 17 \quad \equiv 19 \quad \equiv 20 \quad \equiv 21 \quad \equiv 22 \quad \equiv 23 \] Write in terms of \( i \). Simplify your answer as much as possible. \[ -\sqrt{-80} \]

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