Introduction
Properties of square numbers are explained with examples in this article. Square numbers are numbers that are obtained when a number is multiplied by itself. For example, 9 is a square number that is produced when 3 is multiplied by itself. The number that is to be squared is represented by writing a two as a superscript to the number under consideration. The number that is squared by itself is expressed as:
\(3\times 3=9=3^2\) [Three squared equals 9]
Square of Numbers from 1 to 50
Here is the list of square numbers from 1 to 50, where N is the natural number and N\(^2\) is the square of N. The list will help us to learn about the properties of square numbers.
What are the Properties of Square Numbers?
The properties of square numbers are as follows. Verify each of the properties by taking a look at the table.
- Square numerals have 0, 1, 4, 5, 6, or 9 at the units place. If you check the table above this property can easily be verified. A number’s square will always have a 1 at the end if it ends in 1 or 9.
- A number’s square will always end with 6 if it ends in 4 or 6.
- The unit digit of a square number will always be the square of the unit digit of the number.
- The square root of a perfect square is always a natural number.
- An even number of zeros are associated with perfect squares.
- Even numbers when squared always result in even numbers.
- Odd numbers when squared always result in odd numbers.
Solved examples
Example 1: What is the square of 5 and 13?
Solution:
Square of \(5=5^2=25\)
Square of \(13=13^2=169\)
Example 2: Out of the following which of the numbers can be considered to be perfect squares.
100, 111, 120, 121
Solution: Out of the number given above, 100 and 121 are perfect squares. This is because the square root of both these numbers are 10 and 11 which are whole numbers.
Example 3: Gary was asked to transfer some boxes with the help of nine other friends. It takes each person five minutes to transfer one box from the starting point to the destination. How much time would it take to transfer the boxes, if the number of boxes is ten times the number of people available.
Solution:
As stated in the question,
Total number of people including Gary = 1 + 9 = 10,
Time taken to transfer 1 box = 5 minutes,
Number of boxes = 10 x 10 = 100 boxes,
The time taken to transfer one hundred boxes is as follows
Time taken to transfer 100 boxes = 5 x 100 = 500 minutes
Therefore, the time taken to transfer 100 boxes is 500 minutes.
Rapid Recall
The square number of a number is obtained when a number is multiplied by itself. The square root of a number is the process of finding the number that was multiplied by itself to obtain the square number under consideration.
The properties related to the squares of odd and even numbers states that the squares of even numbers are always even numbers and the squares of odd numbers are always odd numbers.
Yes, the number 49 is a perfect square since seven times seven gives us 49.