$$\sqrt{ \frac{ 1 }{ 3 } } - \sqrt{ \frac{ 1 }{ 2 } } + \sqrt{ \frac{ 8 }{ 4 } }$$
$\frac{2\sqrt{3}+3\sqrt{2}}{6}\approx 1.28445705$
$$\frac{\sqrt{1}}{\sqrt{3}}-\sqrt{\frac{1}{2}}+\sqrt{\frac{8}{4}}$$
$$\frac{1}{\sqrt{3}}-\sqrt{\frac{1}{2}}+\sqrt{\frac{8}{4}}$$
$$\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{\frac{1}{2}}+\sqrt{\frac{8}{4}}$$
$$\frac{\sqrt{3}}{3}-\sqrt{\frac{1}{2}}+\sqrt{\frac{8}{4}}$$
$$\frac{\sqrt{3}}{3}-\frac{\sqrt{1}}{\sqrt{2}}+\sqrt{\frac{8}{4}}$$
$$\frac{\sqrt{3}}{3}-\frac{1}{\sqrt{2}}+\sqrt{\frac{8}{4}}$$
$$\frac{\sqrt{3}}{3}-\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt{\frac{8}{4}}$$
$$\frac{\sqrt{3}}{3}-\frac{\sqrt{2}}{2}+\sqrt{\frac{8}{4}}$$
$$\frac{\sqrt{3}}{3}-\frac{\sqrt{2}}{2}+\sqrt{2}$$
$$\frac{2\sqrt{3}}{6}-\frac{3\sqrt{2}}{6}+\sqrt{2}$$
$$\frac{2\sqrt{3}-3\sqrt{2}}{6}+\sqrt{2}$$
$$\frac{2\sqrt{3}-3\sqrt{2}}{6}+\frac{6\sqrt{2}}{6}$$
$$\frac{2\sqrt{3}-3\sqrt{2}+6\sqrt{2}}{6}$$
$$\frac{2\sqrt{3}+3\sqrt{2}}{6}$$
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