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

(Video Solution)
(Video Solution)
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<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>.
 
<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>.
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==Video Solution (CREATIVE THINKING!!!)==
 +
https://youtu.be/elN5lYfeKnw
 +
 +
~Education, the Study of Everything
 +
 
==Video Solution==
 
==Video Solution==
 
https://youtu.be/cY4NYSAD0vQ
 
https://youtu.be/cY4NYSAD0vQ

Revision as of 16:39, 31 March 2023

Problem

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

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

Solution

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

Video Solution (CREATIVE THINKING!!!)

https://youtu.be/elN5lYfeKnw

~Education, the Study of Everything

Video Solution

https://youtu.be/cY4NYSAD0vQ

https://youtu.be/H0WHiLy1cFg

~savannahsolver

See Also

2017 AMC 8 (ProblemsAnswer KeyResources)
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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