[tex]\textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=\sqrt{125}\\ \qquad \sqrt{5^2\cdot 5}\\ \qquad 5\sqrt{5}\\ w=3\sqrt{5}-4\sqrt{12}\\ \qquad 3\sqrt{5}-4\sqrt{2^2\cdot 3}\\ \qquad 3\sqrt{5}-8\sqrt{3} \end{cases}\implies \begin{array}{llll} A=(5\sqrt{5})(3\sqrt{5}-8\sqrt{3})\\\\ A=15(\sqrt{5})^2-40\sqrt{3}\cdot \sqrt{5}\\\\ A=15\sqrt{5^2}-40\sqrt{3\cdot 5}\\\\ A=15\cdot 5-40\sqrt{15}\\\\ A=75-40\sqrt{15} \end{array}[/tex]
