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.
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.