AMC8 2017

AMC8 2017 · Q3

AMC8 2017 · Q3. It mainly tests Exponents & radicals.

What is the value of the expression ?

求这个表达式的值？

(A) 4 4

(B) $4\sqrt{2}$ $4\sqrt{2}$

(D) $8\sqrt{2}$ $8\sqrt{2}$

(E) 16 16

Answer

Correct choice: (C)

正确答案：（C）

Solution

$\sqrt{16\sqrt{8\sqrt{4}}}$ = $\sqrt{16\sqrt{8\cdot 2}}$ = $\sqrt{16\sqrt{16}}$ = $\sqrt{16\cdot 4}$ = $\sqrt{64}$ = $\boxed{\textbf{(C)}\ 8}$.

$\sqrt{16\sqrt{8\sqrt{4}}}$ = $\sqrt{16\sqrt{8\cdot 2}}$ = $\sqrt{16\sqrt{16}}$ = $\sqrt{16\cdot 4}$ = $\sqrt{64}$ = $\boxed{\textbf{(C)}\ 8}$。

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