$$(2 \sqrt{ 3 } -4 \sqrt{ 5 } )(2 \sqrt{ 5 } -3 \sqrt{ 3 }$$
$16\sqrt{15}-58\approx 3.967733539$
$$4\sqrt{3}\sqrt{5}-6\left(\sqrt{3}\right)^{2}-8\left(\sqrt{5}\right)^{2}+12\sqrt{3}\sqrt{5}$$
$$4\sqrt{15}-6\left(\sqrt{3}\right)^{2}-8\left(\sqrt{5}\right)^{2}+12\sqrt{3}\sqrt{5}$$
$$4\sqrt{15}-6\times 3-8\left(\sqrt{5}\right)^{2}+12\sqrt{3}\sqrt{5}$$
$$4\sqrt{15}-18-8\left(\sqrt{5}\right)^{2}+12\sqrt{3}\sqrt{5}$$
$$4\sqrt{15}-18-8\times 5+12\sqrt{3}\sqrt{5}$$
$$4\sqrt{15}-18-40+12\sqrt{3}\sqrt{5}$$
$$4\sqrt{15}-58+12\sqrt{3}\sqrt{5}$$
$$4\sqrt{15}-58+12\sqrt{15}$$
$$16\sqrt{15}-58$$
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$2 {(8 \sqrt{15} - 29)} = 3.967733539$
