2016 AMC 8 Problems/Problem 7: Difference between revisions
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==Problem== | |||
Which of the following numbers is not a perfect square? | Which of the following numbers is not a perfect square? | ||
<math>\textbf{(A) }1^{2016}\qquad\textbf{(B) }2^{2017}\qquad\textbf{(C) }3^{2018}\qquad\textbf{(D) }4^{2019}\qquad \textbf{(E) }5^{2020}</math> | <math>\textbf{(A) }1^{2016}\qquad\textbf{(B) }2^{2017}\qquad\textbf{(C) }3^{2018}\qquad\textbf{(D) }4^{2019}\qquad \textbf{(E) }5^{2020}</math> | ||
==Solution== | ==Solution 1== | ||
Our answer must have an odd exponent in order for it to not be a square. Because <math>4</math> is a perfect square, <math>4^{2019}</math> is also a perfect square, so our answer is <math>\boxed{\textbf{(B) }2^{2017}}</math>. | Our answer must have an odd exponent in order for it to not be a square. Because <math>4</math> is a perfect square, <math>4^{2019}</math> is also a perfect square, so our answer is <math>\boxed{\textbf{(B) }2^{2017}}</math>. | ||
==Video Solution== | |||
https://youtu.be/ymZQgW-cL4s?si=NbFD5ZIPgtojqEaj | |||
~Elijahman~ | |||
==Video Solution (CREATIVE THINKING!!!)== | |||
https://youtu.be/_zfiULRR3co | |||
~Education, the Study of Everything | |||
==Video Solution== | |||
https://www.youtube.com/watch?v=BZKzpY_pH5A ~David | |||
https://youtu.be/prtDHdc12cs | |||
~savannahsolver | |||
==See Also== | |||
{{AMC8 box|year=2016|num-b=6|num-a=8}} | {{AMC8 box|year=2016|num-b=6|num-a=8}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
[[Category:Introductory Algebra Problems]] | |||
Latest revision as of 17:02, 25 June 2025
Problem
Which of the following numbers is not a perfect square?
Solution 1
Our answer must have an odd exponent in order for it to not be a square. Because 
is a perfect square, 
is also a perfect square, so our answer is 
.
Video Solution
https://youtu.be/ymZQgW-cL4s?si=NbFD5ZIPgtojqEaj
~Elijahman~
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution
https://www.youtube.com/watch?v=BZKzpY_pH5A ~David
~savannahsolver
See Also
| 2016 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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. Error creating thumbnail: File missing
