Difference between revisions of "2017 AMC 8 Problems/Problem 3"

Revision as of 15:27, 22 November 2017

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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All AJHSME/AMC 8 Problems and Solutions

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 ==Solution==
-To solve the equation<math>\sqrt{16\sqrt{8\sqrt{4}}}</math>. The square root of four is <math>2</math>. Multiply this by <math>8</math> to get <math>16</math>, and the square root of sixteen is <math>4</math>, and multiply this by <math>16</math> to get <math>64</math>. The square root of <math>64</math> is <math>8</math>, hence the answer (C).
+<math>\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}.</math>
-~pegasuswa
 ==See Also==