$$8+ \sqrt{ 1 \sqrt{ 7 \sqrt{ 0 } } }$$
$8$
$$8+\sqrt{1\sqrt{7\times 0}}$$
$$8+\sqrt{1\sqrt{0}}$$
$$8+\sqrt{1\times 0}$$
$$8+\sqrt{0}$$
$$8+0$$
$$8$$
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$2^{3}$