Question

write in terms of i. simplify your answer as much as possible. $sqrt{-96}$

Explanation:

Step1: Recall the definition of $i$

Recall that $i = \sqrt{- 1}$. We can rewrite $\sqrt{-36}$ as $\sqrt{36\times(-1)}$.

Step2: Use the square - root property

By the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (where $a = 36$ and $b=-1$ and $a\geq0$), we have $\sqrt{36\times(-1)}=\sqrt{36}\cdot\sqrt{-1}$.

Step3: Simplify the square - roots

Since $\sqrt{36}=6$ and $\sqrt{-1}=i$, then $\sqrt{36}\cdot\sqrt{-1}=6i$.

Answer:

$6i$