$$( \sqrt{ 7 } + \sqrt{ 2 } +1)( \sqrt{ 7 } -1- \sqrt{ 2 } )$$
$4-2\sqrt{2}\approx 1.171572875$
$$\left(\sqrt{7}\right)^{2}-\sqrt{7}-\sqrt{7}\sqrt{2}+\sqrt{2}\sqrt{7}-\sqrt{2}-\left(\sqrt{2}\right)^{2}+\sqrt{7}-1-\sqrt{2}$$
$$7-\sqrt{7}-\sqrt{7}\sqrt{2}+\sqrt{2}\sqrt{7}-\sqrt{2}-\left(\sqrt{2}\right)^{2}+\sqrt{7}-1-\sqrt{2}$$
$$7-\sqrt{7}-\sqrt{14}+\sqrt{2}\sqrt{7}-\sqrt{2}-\left(\sqrt{2}\right)^{2}+\sqrt{7}-1-\sqrt{2}$$
$$7-\sqrt{7}-\sqrt{14}+\sqrt{14}-\sqrt{2}-\left(\sqrt{2}\right)^{2}+\sqrt{7}-1-\sqrt{2}$$
$$7-\sqrt{7}-\sqrt{2}-\left(\sqrt{2}\right)^{2}+\sqrt{7}-1-\sqrt{2}$$
$$7-\sqrt{7}-\sqrt{2}-2+\sqrt{7}-1-\sqrt{2}$$
$$5-\sqrt{7}-\sqrt{2}+\sqrt{7}-1-\sqrt{2}$$
$$5-\sqrt{2}-1-\sqrt{2}$$
$$4-\sqrt{2}-\sqrt{2}$$
$$4-2\sqrt{2}$$
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