2016 AMC 8 Problems/Problem 7
Problem
Which of the following numbers is not a perfect square?
Video Solution
https://www.youtube.com/watch?v=BZKzpY_pH5A
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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
.
Solution 2
We know that in order for something to be a perfect square, it can be written as for
. So, if we divide all of the exponents by 2, we can see which ones are perfect squares, and which ones are not.
,
,
,
,
. Since we know that 4 is a perfect square itself, we know that even though the integer number is odd, the number that it becomes will be a perfect square. This is because
. this is also a perfect square because the exponent
is even, and the base
is also a perfect square, thus
is a perfect square. So, that only leaves us with one choice,
.
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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 |
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