Problem:
Which of the following numbers is not a perfect square?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The numbers have even exponents and hence are squares. The number is not a perfect square because it is twice a square . SInce , it is also a perfect square.
A positive integer power of a square is again a square. This eliminates choices and . An even power of any integer is a square. This eliminates choices and . The only remaining choice is , and in fact, an odd power of a non-square cannot be a square.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions