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  3. You know that x is a positive integer. Which of the following statements individually provide(s)sufficient additional informatio

You know that x is a positive integer. Which of the following statements individually provide(s)sufficient additional informatio

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问题 You know that x is a positive integer. Which of the following statements individually provide(s)sufficient additional information to determine whether the square root of x is also an integer? Select all such statements.
选项 A、x is the square of an integer.
B、The square root of x is the square of an integer.
C、0
答案A, B
解析 The correct answer is A and B. Statement(A)can be expressed as x-t2, where t is any nonzero integer. In this case, the square root of x equals the square root of t2, which is t or -t, depending on whether t is positive or negative, respectively. In either case, the square root of x is an integer. Therefore, statement(A)alone is sufficient. Statement(B)is also sufficient because the square of an integer must also be an integer. Statement(C)indicates that x is a positive integer less than 10, which is not sufficient to determine whether the square root of x is also an integer.
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