[tex]\bf \sqrt{125}\div \sqrt{5}\implies \cfrac{\sqrt{125}}{\sqrt{5}}\qquad \begin{cases} 125=&5\cdot 5\cdot 5\\ &5^2\cdot 5 \end{cases}\implies \cfrac{\sqrt{5^2\cdot 5}}{\sqrt{5}} \\\\\\ \cfrac{5~~\begin{matrix} \sqrt{5} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} \sqrt{5} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 5[/tex]
