Simplify this equation if $x$ is negative I am trying to simplify $7 \cdot\sqrt{5x}\cdot\sqrt{180x^5}$, given that $x$ is negative. The answer is $-210x^3$, but I am getting $210x^3$. Below is my reasoning:
For a $ k > 0 $, let $ k = - x $. Then, $7\cdot\sqrt{5x}\cdot\sqrt{180x^5}$ = $7\cdot5\cdot6\cdot i\sqrt{k} \cdot i\sqrt{k^5}$ = $210\cdot(-1)\cdot k^3$ = $ 210 \cdot (-1) \cdot k^3 = 210\cdot (-1) \cdot (-x)^3 = 210x^3$.
What am I doing wrong?
Any help is greatly appreciated

$$\text{$7 \cdot\sqrt{5x}\cdot\sqrt{180x^5} \ $ where $ \ x<0$}$$
Lets let $x=-1$ to see what we should expect.
\begin{align}
   \left. \left( 7 \cdot\sqrt{5x}\cdot\sqrt{180x^5}\right)\right|_{x=-1}
   &= 7 \cdot\sqrt{-5}\cdot\sqrt{-180} \\
   &=  7 \cdot i \cdot\sqrt{5}\cdot i \cdot \sqrt{180} \\
   &= -7 \cdot \sqrt{900} \\
   &= -210
\end{align}
Now Lets do it with $x=-n$ where $n > 0$.
\begin{align}
   \left. \left( 7 \cdot\sqrt{5x}\cdot\sqrt{180x^5}\right)\right|_{x=-n}
   &= 7 \cdot\sqrt{-5n}\cdot\sqrt{-180n^5} \\
   &=  7 \cdot i \cdot\sqrt{5n}\cdot i \cdot \sqrt{180n^5} \\
   &= -7 \cdot \sqrt{900n^6} \\
   &= -210n^3 \\
   &= -210(-x)^3 \\
   &= 210x^3
\end{align}
