List all the perfect squares between 1 and 250
The Correct Answer and Explanation is:
The perfect squares between 1 and 250 are numbers that can be expressed as the square of an integer. These numbers are generated by squaring whole numbers, which means multiplying a number by itself.
To identify the perfect squares between 1 and 250, let’s first list the integers whose squares fall within this range. The square of an integer (n) is written as (n^2).
Perfect squares from (1^2) to (15^2):
- (1^2 = 1)
- (2^2 = 4)
- (3^2 = 9)
- (4^2 = 16)
- (5^2 = 25)
- (6^2 = 36)
- (7^2 = 49)
- (8^2 = 64)
- (9^2 = 81)
- (10^2 = 100)
- (11^2 = 121)
- (12^2 = 144)
- (13^2 = 169)
- (14^2 = 196)
- (15^2 = 225)
So, the perfect squares between 1 and 250 are:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, and 225.
Explanation:
- Definition of Perfect Squares: A perfect square is a number that can be written as the square of an integer. For example, ( 4 = 2^2 ), ( 9 = 3^2 ), and so on.
- Identifying Perfect Squares: To find the perfect squares between 1 and 250, we calculate the squares of integers starting from 1. Since ( 15^2 = 225 ) is the largest perfect square less than 250, we stop at ( 15^2 ).
- Range: The smallest perfect square is ( 1^2 = 1 ), and the largest is ( 15^2 = 225 ), which are all within the range of 1 to 250.
- Real-World Application: Perfect squares are used in various areas of mathematics, including geometry, algebra, and number theory. They also frequently appear in problems related to area, volume, and patterns in number sequences.
Thus, these perfect squares represent all the numbers between 1 and 250 that are the square of an integer.