Difference between revisions of "2017 AMC 8 Problems/Problem 3"
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==Solution 1== | ==Solution 1== | ||
| − | <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{ | + | <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>. |
==Worse Solution== | ==Worse Solution== | ||
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{{MAA Notice}} | {{MAA Notice}} | ||
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| + | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 19:00, 7 June 2025
Contents
Problem
What is the value of the expression 
?
Solution 1
= 
= 
= 
= 
= 
.
Worse Solution
~ Sahan
We solve the general form expression 
. Note,
![\[\sqrt{a\sqrt{b\sqrt{c}}}=(a^4b^2c^1)^\frac{1}{8}\]](http://latex.artofproblemsolving.com/4/2/4/424d5de402446a916dcfea1b75d7b3806764116b.png)
Thus our answer is,
![\[(16^4\cdot8^24^1)^\frac{1}{8}=16777216^{\frac{1}{8}}=8\]](http://latex.artofproblemsolving.com/2/3/8/23837ddc992819d2722cda055f450a33918d8fe6.png)
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
