$$(3 \sqrt{ 2 } +5 \sqrt{ 3 } )+( \sqrt{ 2 } + \sqrt{ 3 }$$
$2\left(5-\sqrt{6}\right)\left(\sqrt{2}+\sqrt{3}\right)\approx 16.049159095$
$$4\sqrt{2}+5\sqrt{3}+\sqrt{3}$$
$$4\sqrt{2}+6\sqrt{3}$$
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