Hey everyone, this is problem one, grades 11 through 12, on the 2025 Math Kangaroo. So, the year 2025 is a perfect square because 2025 equals 45 squared. How many years will pass until the next perfect square year? We have A, 25, B, 91, C, 121, D, 500, and E, 2025. Okay, so how should we approach this problem? Well, we're given initially that 2025 is a perfect square, it's equal to 45 squared. And if we know anything about perfect squares, well, they're just the squares of integers. So, the next perfect square should actually just be 46 squared. We can do a little bit of computation to obtain that 46 squared is equal to 2116. And, well, to obtain, like, the number of years we need to get to that, it's the year 2025, so we just subtract, and we obtain 91 years. Alternatively, if you don't want to do such a large subtraction, you can do some difference of two squares, and we obtain 46 minus 45 times 46 plus 45 is equal to 46 squared minus 45 squared is equal to 91. So, either way, B is our answer.

Math Kangaroo

perfect square

2025

46 squared

91 years