A Perfect Square

An old problem from the Soviet Mathematical Olympiad:

Find the 4-digit number aabb that is a perfect square.

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The smallest 4-digit perfect square is 1024 (32²). The largest is 9801 (99²). And aabb = 1000a + 100a + 10b + b = 1100a + 11b = 11(100a + b). So 11 is one of the factors of aabb, and aabb is of the form (11k)². That leaves only six candidates to check (33², 44², 55², 66², 77², 88²), and it turns out the answer is 88² = 7744. (Thanks, Danesh.)