Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2016 AMC 8 Problems/Problem 7"
 
(35 intermediate revisions by 15 users not shown)
Line 1: Line 1:
 +
==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==
−
{{solution}}
+
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 (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}}

Latest revision as of 22:00, 17 May 2024

Problem

Which of the following numbers is not a perfect square?

$\textbf{(A) }1^{2016}\qquad\textbf{(B) }2^{2017}\qquad\textbf{(C) }3^{2018}\qquad\textbf{(D) }4^{2019}\qquad \textbf{(E) }5^{2020}$

Solution 1

Our answer must have an odd exponent in order for it to not be a square. Because $4$ is a perfect square, $4^{2019}$ is also a perfect square, so our answer is $\boxed{\textbf{(B) }2^{2017}}$.

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

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

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2016_AMC_8_Problems/Problem_7&oldid=219416"