2017 AMC 8 Problems/Problem 3

Problem 3

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

$\textbf{(A) }4\qquad\textbf{(B) }4\sqrt{2}\qquad\textbf{(C) }8\qquad\textbf{(D) }8\sqrt{2}\qquad\textbf{(E) }16$

$\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}.

2017 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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