How many perfect squares are between 1600 and 3600? This question may seem straightforward, but it requires a bit of mathematical analysis to find the exact number. In this article, we will explore the process of determining the count of perfect squares within the given range and shed light on the fascinating world of numbers.
The first step in solving this problem is to identify the smallest and largest perfect squares within the range of 1600 to 3600. To do this, we need to find the square roots of the lower and upper bounds, which are 1600 and 3600, respectively.
The square root of 1600 is 40, and the square root of 3600 is 60. Since we are looking for perfect squares, we need to find the integers between 40 and 60 (inclusive) whose squares will fall within the given range.
To find the count of perfect squares between 1600 and 3600, we can use the following formula:
Count of perfect squares = (largest integer – smallest integer) + 1
In this case, the largest integer is 60, and the smallest integer is 40. Plugging these values into the formula, we get:
Count of perfect squares = (60 – 40) + 1 = 21
Therefore, there are 21 perfect squares between 1600 and 3600. Some of these squares include 1600 (40^2), 2250 (45^2), 2560 (48^2), and so on, up to 3600 (60^2).
This exercise not only helps us understand the distribution of perfect squares within a given range but also highlights the beauty of mathematics. By exploring the properties of numbers and applying simple formulas, we can uncover fascinating patterns and relationships that exist in the world around us.
