What is the greatest perfect square between 250 and 300? This question may seem simple at first glance, but it requires a bit of mathematical exploration to find the answer. In this article, we will delve into the world of perfect squares and determine which one lies within the specified range.
The first step in finding the greatest perfect square between 250 and 300 is to identify the square roots of these numbers. The square root of 250 is approximately 15.81, while the square root of 300 is approximately 17.32. Since we are looking for a perfect square, we need to find a whole number that, when squared, falls between these two square roots.
To do this, we can start by rounding up the square root of 250 to the nearest whole number, which is 16. Squaring 16 gives us 256, which is the first perfect square greater than 250. Now, we need to find the next perfect square, which will be the greatest one between 250 and 300.
We can continue this process by rounding up the square root of 300 to the nearest whole number, which is 18. Squaring 18 gives us 324, which is greater than 300. However, we are looking for the greatest perfect square between 250 and 300, so we need to find the square root of 300 and round it down to the nearest whole number, which is 17. Squaring 17 gives us 289, which is the perfect square we are looking for.
In conclusion, the greatest perfect square between 250 and 300 is 289. This number is the result of squaring 17, and it lies within the specified range, making it the answer to our question.
