$$\frac{\sqrt{3}}{2+5\sqrt{3}}$$
$\frac{15-2\sqrt{3}}{71}\approx 0.162477442$
$$\frac{\sqrt{3}\left(2-5\sqrt{3}\right)}{\left(2+5\sqrt{3}\right)\left(2-5\sqrt{3}\right)}$$
$$\frac{\sqrt{3}\left(2-5\sqrt{3}\right)}{2^{2}-\left(5\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(2-5\sqrt{3}\right)}{4-\left(5\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(2-5\sqrt{3}\right)}{4-5^{2}\left(\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(2-5\sqrt{3}\right)}{4-25\left(\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(2-5\sqrt{3}\right)}{4-25\times 3}$$
$$\frac{\sqrt{3}\left(2-5\sqrt{3}\right)}{4-75}$$
$$\frac{\sqrt{3}\left(2-5\sqrt{3}\right)}{-71}$$
$$\frac{2\sqrt{3}-5\left(\sqrt{3}\right)^{2}}{-71}$$
$$\frac{2\sqrt{3}-5\times 3}{-71}$$
$$\frac{2\sqrt{3}-15}{-71}$$
$$\frac{-2\sqrt{3}+15}{71}$$
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