Question

write in terms of i. simplify your answer as much as possible. $sqrt{-39}$

Explanation:

Step1: Recall the definition of $i$

We know that $i = \sqrt{- 1}$, and $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ for $a\geq0,b\geq0$. For $\sqrt{-39}$, we can rewrite it as $\sqrt{39\times(-1)}$.

Step2: Apply the square - root property

$\sqrt{-39}=\sqrt{39}\cdot\sqrt{-1}$.

Step3: Substitute $i$

Since $\sqrt{-1}=i$, we have $\sqrt{-39}=i\sqrt{39}$.

Answer:

$i\sqrt{39}$