How many perfect squares are there from 1 to 100? This question may seem simple at first glance, but it requires a deeper understanding of mathematics to answer accurately. In this article, we will explore the concept of perfect squares and determine the number of such numbers within the given range.
A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are all perfect squares because they can be written as 1^2, 2^2, 3^2, 4^2, and 5^2, respectively. To find the number of perfect squares between 1 and 100, we need to identify the largest integer whose square is less than or equal to 100.
Let’s start by determining the square root of 100. The square root of 100 is approximately 10, which means that the largest integer whose square is less than or equal to 100 is 10. Now, we need to count the number of integers from 1 to 10, inclusive, as these will be the perfect squares within the given range.
There are 10 integers from 1 to 10, which are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Since each of these integers has a corresponding perfect square, we can conclude that there are 10 perfect squares between 1 and 100.
In conclusion, the answer to the question ‘How many perfect squares are there from 1 to 100?’ is 10. This demonstrates the importance of understanding the properties of perfect squares and the relationship between integers and their squares. By identifying the largest integer whose square is less than or equal to the given number, we can easily determine the number of perfect squares within that range.
