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.
Table of Contents
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.
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 $X=n^2$ for some natural number $n.$
• The square root of a perfect square must have unit digit $0, 1, 4, 5$ 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 $\sqrt{8}=2\sqrt{2}$ is not an integer, $8$ is an example of non-perfect square numbers, and the square root $\sqrt{8}$ is a quadratic surd.
List of Perfect Squares
| 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 |
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.