$$(2\sqrt{7}-4\sqrt{3})^{2}$$
$76-16\sqrt{21}\approx 2.678788881$
$$4\left(\sqrt{7}\right)^{2}-16\sqrt{7}\sqrt{3}+16\left(\sqrt{3}\right)^{2}$$
$$4\times 7-16\sqrt{7}\sqrt{3}+16\left(\sqrt{3}\right)^{2}$$
$$28-16\sqrt{7}\sqrt{3}+16\left(\sqrt{3}\right)^{2}$$
$$28-16\sqrt{21}+16\left(\sqrt{3}\right)^{2}$$
$$28-16\sqrt{21}+16\times 3$$
$$28-16\sqrt{21}+48$$
$$76-16\sqrt{21}$$
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$76-16\sqrt{21}$