Question

write in terms of i. simplify your answer as much as possible. $sqrt{-75}$

Explanation:

Step1: Rewrite -75 as product

We know that $\sqrt{-75}=\sqrt{-1\times75}$.

Step2: Use square - root property

By the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = - 1$, $b = 75$), we have $\sqrt{-1\times75}=\sqrt{-1}\times\sqrt{75}$.

Step3: Recall the definition of $i$

Since $\sqrt{-1}=i$, and $\sqrt{75}=\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}=5\sqrt{3}$.

Step4: Combine the results

So $\sqrt{-75}=i\times5\sqrt{3}=5i\sqrt{3}$.

Answer:

$5i\sqrt{3}$