The square of an integer is called a perfect square number. If (x) is the perfect square of an integer, then what is the perfect square of its next integer?

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A (x + 1)
B (x² + 1)
C (x² + 2x + 1)
D (x + 2√x + 1)

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Answer: D. (x + 2√x + 1)

Let the integer be n. Then x = n². The next integer is n + 1. Its perfect square is (n + 1)² = n² + 2n + 1. Since n² = x and n = √x, the expression becomes x + 2√x + 1.

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The square of an integer is called a perfect square number. If (x) is the perfect square of an integer, then what is the perfect square of its next integer?

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