**Definition of Perfect Square**

A perfect square is a number, from a given number system, that can be shown as the square of a number from the same number system.

**or**

A perfect square is a number that can be expressed as the product of 2 equivalent integers.

**For instance:**

**36 is a perfect square.**

**36** is a natural number, and since there is another natural number **6**, such as

6=^{2}36

**36** is a perfect square.

or

As** 36** is a natural number and the square root of **36** is a natural number **6**. So, **36** is a perfect square.

**is a perfect square.**

is a rational number, and since there is another rational number which is , such that

is a perfect square.

or

As** ** is a rational number and the square root of is another rational number . So, is a perfect square.

**How to Justify If a Number Is a Perfect Square**

You can say if a number is a perfect square in many different ways.

- First of all, if you find a square by the multiplication of two equal integers by each other, the product is a perfect square.

**Example:**

1*1 is a perfect square. So as 5*5 and 100*100.

- You can also say if a number is a perfect square by calculating its square roots. Calculating the square root is the opposite of squaring a number.
- If you Calculate the square root of a number and it is a whole number, that shows you that the number is a perfect square.

**For instance:**

The square root of 49 is 7. The square root of 50 is not a whole number. So, 50 is not a perfect square.

**Understanding Perfect Squares**

- A perfect square is a number that can be shown as the multiplication of two equal or same integers.

**NOT Perfect Squares**

If you calculate the square root of any number and do not get a whole number as a result, the number whose square root you are Calculating is not a Perfect Square.

**Examples:**

**22 is NOT a perfect square.**

As 22 is a natural number, but the square root of 22 is not a natural number (it is an irrational number that never terminates nor repeats [4.69041575982 …]). Hence, 22 is NOT a perfect square.

** is not a perfect square**

Since is a natural number, but the square root of is not a natural number (it is an irrational number that never terminates nor repeats [0.96824583655…]), is NOT a perfect square.

** **