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Problem 652

AMC 10/12, early questions

Algebra Difficulty 3.8 Multiple choice China Mathematical Competition (Shaanxi) · China

A new sequence is obtained from the sequence of the positive integers $\{1, 2, 3, \ldots\}$ by deleting all the perfect squares. Then the $2\ 003$ rd term of the new sequence is:

Pick one

Official solution

Since $\sqrt{2046} = \sqrt{2047} = \sqrt{2048} = \sqrt{2049} = 45$ , and $2003 + 45 = 2048$ , Answer: C.

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