Question

write in terms of i. simplify your answer as much as possible. $sqrt{-144}$

Explanation:

Step1: Recall the definition of $i$

We know that $i=\sqrt{- 1}$ and $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ for $a\geq0,b\geq0$. So, $\sqrt{-144}=\sqrt{144\times(-1)}$.

Step2: Apply the square - root property

Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$, we have $\sqrt{144\times(-1)}=\sqrt{144}\cdot\sqrt{-1}$.

Step3: Simplify the square - roots

Since $\sqrt{144} = 12$ and $\sqrt{-1}=i$, then $\sqrt{144}\cdot\sqrt{-1}=12i$.

Answer:

$12i$