A perfect square is a concept that is closely related to the concept of square root. We usually learn about perfect squares and square roots in the chapter on exponents. In a layman’s language, a perfect square can be defined as any positive integer that can be expressed as the product of two same numbers. These numbers can either be positive or negative, as the case may be. Let us understand perfect squares with the help of some examples. 144 is a perfect square since it can be expressed as the product of two same numbers i.e 12 * 12 and -12 * -12. Similarly, 225 is a perfect square since it can be expressed as the product of two same numbers i.e 15 * 15 and -15 * -15. In this article, we will discuss the process through which perfect squares can be identified easily, but before that, let us learn in brief the concept of square root.
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What Do You Mean by Square Root?
The square root is a very easy concept to understand. The square root of a number can be defined as an inverse or opposite operation of squaring a number. When a square root of a number is multiplied by itself, we get the original number. Let us take some examples to understand the concept of square roots clearly. The square root of 121 is 11 because the multiplication of 11 with itself gives us 121. Similarly, the square root of 256 is 16 because multiplication of 16 with itself gives us 256. The concept of square roots is very important since it helps us in understanding the perfect squares and the perfect cube.
Process of Identification of Perfect Square
While going through the perfect square numbers of the first 20 natural numbers, we can observe some common patterns in all of them. These patterns are very useful in the identification of perfect squares. The following points given below can be used as a process to identify various perfect square numbers.
- For the numbers that end with the digits 7 and 3, we will have the number 9 in the units place digit of its square number. For example, the square root of 1369 is 37, thus ending with the digit 9.
- For the numbers that end with the digit 5, we will have 5 in the units place digit of its square number. For example, the square root of 11025 is 105, thus ending with the digit 5.
- For the numbers that end with the digits 6 and 4, we will have the number 6 in the units place digit of its square number. For example, the square root of 3136 is 56, thus ending with the digit 6.
- For the numbers that end with the digits 8 and 2, we will have the number 4 in the units place digit of its square number. For example, the square root of 1444 is 38, thus ending with the digit 4.
- For the numbers that end with the digits 9 and 1, we will have the number 1 in the units place digit of its square number. For example, the square root of 361 is 19, thus ending with the digit 1.
Some Tips and Tricks Related to Perfect Squares
- A perfect square will always be positive.
- The square roots of perfect square numbers can be both negative and positive.
- We can find the square root of perfect squares using the method of prime factorization.
- Using the method of prime factorization, we can easily find out the cube root of perfect cubes.
If you want to learn more about the concepts of square root and perfect square in detail and in a fun and interesting manner, visit Cuemath and learn from the best teachers of the subject.
