$${ \left(8-3 \sqrt{ 7 } + \frac{ 1 }{ 8-3 \sqrt{ 7 } } \right) }^{ 2 }$$
$256$
$$\left(8-3\sqrt{7}+\frac{8+3\sqrt{7}}{\left(8-3\sqrt{7}\right)\left(8+3\sqrt{7}\right)}\right)^{2}$$
$$\left(8-3\sqrt{7}+\frac{8+3\sqrt{7}}{8^{2}-\left(-3\sqrt{7}\right)^{2}}\right)^{2}$$
$$\left(8-3\sqrt{7}+\frac{8+3\sqrt{7}}{64-\left(-3\sqrt{7}\right)^{2}}\right)^{2}$$
$$\left(8-3\sqrt{7}+\frac{8+3\sqrt{7}}{64-\left(-3\right)^{2}\left(\sqrt{7}\right)^{2}}\right)^{2}$$
$$\left(8-3\sqrt{7}+\frac{8+3\sqrt{7}}{64-9\left(\sqrt{7}\right)^{2}}\right)^{2}$$
$$\left(8-3\sqrt{7}+\frac{8+3\sqrt{7}}{64-9\times 7}\right)^{2}$$
$$\left(8-3\sqrt{7}+\frac{8+3\sqrt{7}}{64-63}\right)^{2}$$
$$\left(8-3\sqrt{7}+\frac{8+3\sqrt{7}}{1}\right)^{2}$$
$$\left(8-3\sqrt{7}+8+3\sqrt{7}\right)^{2}$$
$$\left(16-3\sqrt{7}+3\sqrt{7}\right)^{2}$$
$$16^{2}$$
$$256$$
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$2^{8}$
