[tex]\bf \cfrac{\sqrt{12x^8}}{\sqrt{3x^2}}~~ \begin{cases} 12=&2\cdot 2\cdot 3\\ &2^2\cdot 3\\ x^8=&x^{4\cdot 2}\\ &(x^4)^2 \end{cases}\implies \cfrac{\sqrt{2^2\cdot 3(x^4)^2}}{\sqrt{3x^2}}\implies \cfrac{2\stackrel{x^2}{~~\begin{matrix} x^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} ~~\begin{matrix} \sqrt{3} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ ~~\begin{matrix} \sqrt{3} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 2x^2[/tex]
