<s>[INST] 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
 [/INST] Since $k=-x$, we have $$7\cdot\sqrt{5x}\cdot\sqrt{180x^5}=7\cdot i\cdot\sqrt{5k}\cdot i\sqrt{180k^5}=-7\cdot\sqrt{900k^6}=-7\cdot\sqrt{900x^6}=-210x^3$$
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