$$\frac{\sqrt{2}-\sqrt[3}{\sqrt{3}-1}$$
$\frac{\sqrt{2}+\sqrt{6}-\sqrt{3}-3}{2}\approx -0.434173751$
$$\frac{\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}$$
$$\frac{\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{3}+1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}$$
$$\frac{\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{3}+1\right)}{3-1}$$
$$\frac{\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{3}+1\right)}{2}$$
$$\frac{\sqrt{2}\sqrt{3}+\sqrt{2}-\left(\sqrt{3}\right)^{2}-\sqrt{3}}{2}$$
$$\frac{\sqrt{6}+\sqrt{2}-\left(\sqrt{3}\right)^{2}-\sqrt{3}}{2}$$
$$\frac{\sqrt{6}+\sqrt{2}-3-\sqrt{3}}{2}$$
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