[tex]\cfrac{\sqrt{80}}{\sqrt{20}} ~~ \begin{cases} 80=2\cdot 2\cdot 2\cdot 2\cdot 5\\ \qquad 4\cdot 4\cdot 5\\ \qquad 4^2\cdot 5\\ 20=2\cdot 2\cdot 5\\ \qquad 2^2\cdot 5 \end{cases}\implies \cfrac{\sqrt{4^2\cdot 5}}{\sqrt{2^2\cdot 5}}\implies \cfrac{4\sqrt{5}}{2\sqrt{5}}\implies \cfrac{4}{2}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies 2[/tex]
