Simple Squares

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A "simple square" is any integer greater than 1 that has only three positive integer factors - itself, its square root, and 1. Which of the following is a simple square? (A) 121 (B) 100 (C) 81 (D) 64 (E) 33

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Answer:

Choice A Level of Difficulty E M H The square root of 121 is 11, so if the only factors or 121 are 1, 11, and 121, then 121 is a simple square by definition. The only thing left to determine is whether 121 has any other factors. With a calculator, it's fairly easy to determine that there are no others. So, the only simple square listed is 121, or choice A.

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