Question

simplify. 6\sqrt{-20} enter your answer, in simplest radical form, in the box.

Explanation:

Step1: Rewrite -20 as -1×20

$6\sqrt{-20}=6\sqrt{-1\times20}$

Step2: Use the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = - 1$, $b = 20$)

$6\sqrt{-1\times20}=6\sqrt{-1}\cdot\sqrt{20}$
Since $\sqrt{-1}=i$, we have $6i\sqrt{20}$

Step3: Simplify $\sqrt{20}$

$\sqrt{20}=\sqrt{4\times5}=\sqrt{4}\cdot\sqrt{5}=2\sqrt{5}$
So $6i\sqrt{20}=6i\times2\sqrt{5}=12i\sqrt{5}$

Answer:

$12i\sqrt{5}$