A perfect square number is obtained by the product of two same integers. More specifically, if we multiply an integer with itself then the resultant number will be a perfect square number. So the general form of a perfect square is r2 for some integer r. As 16=42, the number 16 is an example of a perfect square. In this section, we will learn about perfect square numbers.
Definition of Perfect Square
Perfect square definition: A number is called a perfect square if its square root is a whole number. Note that the square root of a perfect square is an integer.
For example, the square root of 4 is 2. Since 2 is an integer, we can say that 4 is a perfect square. More examples of perfect squares: 9, 16, 25, 36, 49, 64, 81 etc.
Perfect Square Examples
From the definition of a perfect square, a number X is called a perfect square if X=x2 for some natural number x. Thus, examples of perfect squares are given below.
- 25=52, so 25 is an example of a perfect square.
- 36 is a perfect square as 36=62.
- 100 is a perfect square as 100 is a square of 10.
- 125 is not a perfect square as it is not a square of some natural numbers.
Non Perfect Square
What is a non-perfect square?
Non perfect square definition: A number is said to be a non perfect square if it is not a square of some natural numbers. In other words, we cannot express it as n2 for some natural number. For example,
- 8 is a non-perfect square as 8=(2√2)2 and 2√2 is not a natural number.
- Non perfect squares 1-100: The numbers from 1 to 100 except 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are examples of non-perfect squares.
Properties of Perfect Squares
• From the definition, the square root of a perfect square is an integer.
• If X is a perfect square, then we can express X as X=n2 for some natural number n.
• The square root of a perfect square must have unit digits 0, 1, 4, 5, or 9.
• The numbers ending with 2, 3, 6, 7, or 8 cannot be a perfect square number. Those numbers are called non-perfect square numbers.
• The square root of a non-perfect square is a quadratic surd. As √8=2√2 is not an integer, 8 is an example of non-perfect square numbers, and the square root √8 is a quadratic surd.
List of Perfect Squares
Perfect square table: We list the perfect squares between 1 and 100 in the table below with proper explanations.
|Integer (n)||n ×n||Perfect square|
Perfect squares from 1 to 100: From the above table, we see that the perfect squares between 1 to 100 are the numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. So there are 10 perfect squares from 1 to 100.