$$\frac{\sqrt{6}}{\sqrt{2+\sqrt{3}}}+\frac{3\sqrt{2}}{\sqrt{6+\sqrt{3}}}-\frac{4\sqrt{3}}{\sqrt{6+}\sqrt{2}}$$
$\frac{\sqrt{396-66\sqrt{3}}}{11}-\frac{2\sqrt{612-102\sqrt{2}}}{17}+3-\sqrt{3}\approx 0.249302864$
