2016 AMC 8 Problems/Problem 7

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

https://youtu.be/ymZQgW-cL4s?si=NbFD5ZIPgtojqEaj

A solution so simple a 12-year-old made it!

~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

2016 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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All AJHSME/AMC 8 Problems and Solutions

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