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2025 Math Kangaroo

Problem 1

Problem 1 · 2025 Math Kangaroo Easy
Number Theory perfect-square

The number 2025 is a perfect square, because \(2025 = 45^2\). How many years will pass until the next year whose number is a perfect square?

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Answer: B — 91
Show hints
Hint 1 of 2
The current year is 45 squared—what is the very next whole number you would square?
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Hint 2 of 2
The gap to the next perfect square is 46² minus 45², which you can get without multiplying out either square.
Show solution
Approach: difference of consecutive squares
  1. The next perfect square after 45² is 46².
  2. The gap equals 46² − 45² = 46 + 45 = 91.
  3. So 91 years pass.
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