perfect-square

3+ Examples to Understand Perfect Square

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

62 = 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.

 

  • \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

perfect-square

 

 

 

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

or

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.

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.

\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.