2017 AMC 8 Problems/Problem 3

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 1

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

Worse Solution

~ Sahan

We solve the general form expression $\sqrt{a\sqrt{b\sqrt{c}}}$ . Note, $\sqrt{a\sqrt{b\sqrt{c}}}=(a^4b^2c^1)^\frac{1}{8}$ Thus our answer is, $(16^4\cdot8^24^1)^\frac{1}{8}=16777216^{\frac{1}{8}}=8$

Video Solution (CREATIVE THINKING!!!)

https://youtu.be/elN5lYfeKnw

~Education, the Study of Everything

Video Solution

https://youtu.be/cY4NYSAD0vQ

https://youtu.be/H0WHiLy1cFg

~savannahsolver

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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