3+ Examples to Understand Perfect Square

Table of Contents Hide

1) Definition of Perfect Square
- 1.1) For instance:
2) How to Justify If a Number Is a Perfect Square
- 2.1) Example:
3) NOT Perfect Squares
- 3.1) Examples:

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.

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

6² = 36

36 is a perfect square.

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

$\frac{16}{25}$ is a perfect square.

$\frac{16}{25}$ is a rational number, and since there is another rational number which is $\frac{4}{5}$ , such that

$\frac{16}{25}$ is a perfect square.

As $\frac{16}{25}$ is a rational number and the square root of $\frac{16}{25}$ is another rational number $\frac{4}{5}$ . So, $\frac{16}{25}$ is a perfect square.

Further Reading: Why Scientific Notation is used?

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.

Further Reading: What is the Distributive Property?

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.

$\frac{15}{16}$ is not a perfect square

Since $\frac{15}{16}$ is a natural number, but the square root of $\frac{15}{16}$ is not a natural number (it is an irrational number that never terminates nor repeats [0.96824583655…]), $\frac{15}{16}$ is NOT a perfect square.