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

Revision as of 18:49, 23 November 2020

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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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-To solve the equation<math>\sqrt{16\sqrt{8\sqrt{4}}}</math>. The square root of four is 2. Multiply this by 8 to get 16, and the square root of sixteen is 4, and multiply this by 16 to get 64. The square root of 64 is 8, hence the answer (C)
+==Problem 3==
+What is the value of the expression <math>\sqrt{16\sqrt{8\sqrt{4}}}</math>?
+<math>\textbf{(A) }4\qquad\textbf{(B) }4\sqrt{2}\qquad\textbf{(C) }8\qquad\textbf{(D) }8\sqrt{2}\qquad\textbf{(E) }16</math>
+==Solution==
+<math>\sqrt{16\sqrt{8\sqrt{4}}}</math> = <math>\sqrt{16\sqrt{8\cdot 2}}</math> = <math>\sqrt{16\sqrt{16}}</math> = <math>\sqrt{16\cdot 4}</math> = <math>\sqrt{64}</math> = <math>\boxed{\textbf{(C)}\ 8}</math>.
+==Video Solution==
+https://youtu.be/cY4NYSAD0vQ
+==See Also==
+{{AMC8 box|year=2017|num-b=2|num-a=4}}
+{{MAA Notice}}