Question

表达式 $\sqrt{16\sqrt{8\sqrt{4}}}$ 的值是多少？

What is the value of the expression $\sqrt{16\sqrt{8\sqrt{4}}}?$

$4$

$4\sqrt{2}$

$8$

$8\sqrt{2}$

$16$

知识点：根式

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这个表达式可化简为 $\begin{align*} \sqrt{16\sqrt{8\sqrt{4}}} &= \sqrt{16\sqrt{16}} \\ &= \sqrt{64}\\ &= 8 \end{align*}$

所以正确答案是 C。

This expression can be reduced as follows: $\begin{align*} \sqrt{16\sqrt{8\sqrt{4}}} &= \sqrt{16\sqrt{16}} \\ &= \sqrt{64}\\ &= 8 \end{align*}$

Thus, C is the correct answer.