# Perfect Square Definition

It is a **whole number** formed by **multiplying** a **number** by itself. In simple words, **Perfect Square** means the **number** that comes out by multiplying a **single **number **two times**. For Example, **16** is a perfect square because it is **formed** by multiplying **4 by 4**.

**Table of Contents**

A **perfect square** or square **number** has great **significance** in different fields of **Mathematics**, especially in **Geometry**. To find the **Area of a square,** the **square number** is used because you have to multiply a **single** number **two times** as the **square** has all sides with equal **length**.

**Note:**

Read about Geometry here.

## Examples of Perfect Squares

4 = 2 x 2

9 = 3 x 3

16 = 4 x 4

25 = 5 x 5

36 = 6 x 6

49 = 7 x 7

64 = 8 x 8

The above-mentioned numbers are perfect squares because these are formed by multiplying the same number with itself.

**Perfect Squares lower than 200**

4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196.

### Fun Facts about Perfect Square

- A perfect
**square**can’t be**negative**in any condition. - The
**square**number always ends up with**0, 1, 4, 5, 6, and 9.** - A
**number**with an even number of**zeros**is always a perfect**square**while a number with the**odd number of zeros**can be a square of any number.**For example**,**100**and**400**are square numbers while**10**and**4000**are not perfect squares. - The
**Square Root**of a perfect**square numbe**r will always be an**integer**.

**Note:**

You can read about Adding Square Roots here.

### How to check if a number is a perfect square or not?

The **easiest **way is to divide the **number** using **prime** factorization. If you are getting a **pair** of the same **prime** numbers as the **divider** of the **number**, it shows that the number is a **perfect square**. If you are getting an **odd number** of prime numbers and are **unable** to write them in **pairs**, it means that the **number** is not a perfect square.

Let us show you a few **examples** for better **understanding**.

**Example 1:**

Check whether **36** is a perfect **square** or not.

**Solution:**

By prime **factorization**, we got the following **numbers** as the **divider** of this number.

36 = 2 x 2 x 3 x 3

We can see that **prime numbers** can be written in the **form** of pairs. It shows that **36 **is a perfect square of the number.

**Example 2:**

Check whether **48** is a **perfect square** or not.

**Solution:**

48 = 2 x 2 x 2 x 2 x 3

We can see that **“3”** doesn’t exist in **pair** format which shows **48** is not a **perfect square**.

### FAQ's

**Can a perfect square be negative?**

No, a square number can’t be negative because the square of two numbers is also a positive whole number.

**What is the opposite of a perfect square?**

The square root is the opposite of a square number or perfect square number.

**Can we get the answer of a square number in decimal format?**

A square number can’t give an answer in the decimal format. It should definitely show a whole number as its answer.