$$(2\sqrt{3}+5\sqrt{2})\times(7\sqrt{2}-4\sqrt{3})$$
$46-6\sqrt{6}\approx 31.303061543$
$$14\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}+35\left(\sqrt{2}\right)^{2}-20\sqrt{3}\sqrt{2}$$
$$14\sqrt{6}-8\left(\sqrt{3}\right)^{2}+35\left(\sqrt{2}\right)^{2}-20\sqrt{3}\sqrt{2}$$
$$14\sqrt{6}-8\times 3+35\left(\sqrt{2}\right)^{2}-20\sqrt{3}\sqrt{2}$$
$$14\sqrt{6}-24+35\left(\sqrt{2}\right)^{2}-20\sqrt{3}\sqrt{2}$$
$$14\sqrt{6}-24+35\times 2-20\sqrt{3}\sqrt{2}$$
$$14\sqrt{6}-24+70-20\sqrt{3}\sqrt{2}$$
$$14\sqrt{6}+46-20\sqrt{3}\sqrt{2}$$
$$14\sqrt{6}+46-20\sqrt{6}$$
$$-6\sqrt{6}+46$$
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$2 {(23 - 3 \sqrt{6})} = 31.303061543$
