$$(3\sqrt{3}-2\sqrt{2})(4\sqrt{2}-2\sqrt{3})$$
$16\sqrt{6}-34\approx 5.191835885$
$$12\sqrt{3}\sqrt{2}-6\left(\sqrt{3}\right)^{2}-8\left(\sqrt{2}\right)^{2}+4\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-6\left(\sqrt{3}\right)^{2}-8\left(\sqrt{2}\right)^{2}+4\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-6\times 3-8\left(\sqrt{2}\right)^{2}+4\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-18-8\left(\sqrt{2}\right)^{2}+4\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-18-8\times 2+4\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-18-16+4\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-34+4\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-34+4\sqrt{6}$$
$$16\sqrt{6}-34$$
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$2 {(8 \sqrt{6} - 17)} = 5.191835885$
