Question

simplify. 4i√(-24) enter your answer, in simplest radical form, in the box.

Explanation:

Step1: Rewrite the square - root of a negative number

Recall that $\sqrt{-a}=\sqrt{a}\times i$ for $a>0$. So, $\sqrt{-24}=\sqrt{24}\times i=\sqrt{4\times6}\times i$.

Step2: Simplify the square - root

Since $\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}$, then $\sqrt{-24}=2\sqrt{6}i$.

Step3: Multiply by the coefficient

We have $4i\sqrt{-24}=4i\times2\sqrt{6}i$. Since $i\times i = - 1$, then $4i\times2\sqrt{6}i=(4\times2\sqrt{6})\times(i\times i)=8\sqrt{6}\times(-1)$.

Answer:

$-8\sqrt{6}$