Question

simplify. 5i\sqrt{-54} enter your answer, in simplest radical form, in the box.

Explanation:

Step1: Rewrite -54 as -1×54

$5i\sqrt{-1\times54}$
Since $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = - 1$, $b = 54$) and $\sqrt{-1}=i$, we have $5i\times i\sqrt{54}$.

Step2: Simplify $i\times i$

We know that $i^2=-1$, so $5i\times i\sqrt{54}=5\times(-1)\sqrt{54}$.

Step3: Factorize 54

$54 = 9\times6$, so $\sqrt{54}=\sqrt{9\times6}=\sqrt{9}\times\sqrt{6}=3\sqrt{6}$.

Step4: Calculate the final result

$5\times(-1)\sqrt{54}=-5\times3\sqrt{6}=-15\sqrt{6}$

Answer:

$-15\sqrt{6}$