# Perfect Squares: Definition, List, Examples, Properties

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 0 0×0=0 0 1 1×1=1 1 2 2×2=4 4 3 3×3=9 9 4 4×4=16 16 5 5×5=25 25 6 6×6=36 36 7 7×7=49 49 8 8×8=64 64 9 9×9=81 81 10 10×10=100 100

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.

Share via: