# Square Numbers: Multiplying with the Same Number: List of Square Numbers (For CBSE, ICSE, IAS, NET, NRA 2022)

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## What Are Square Numbers?

When a number is multiplied by itself, the product is called a ‘Square Number’ .

Why Square Numbers:

As squares have all the sides equal, in a similar manner a square number is the product of two number which are equal (i.e.. the number itself) .

Area of a square

Square number =

Side of square (in cm) | Area of square (in ) |

3 | |

5 | |

7 | |

8 |

Numbers such as , etc. are special numbers as these are the product of a number by itself.

If we express a number (x) in terms of the square of any natural number such as , then x is a square number. For example, 100 can be expressed as , where 10 is a natural number, therefore 100 is a square number. Whereas, the number 45 cannot be called a square number because it is the product of numbers 9 and 5. The number is not multiplied by itself. **Square numbers** can also be called as perfect square numbers.

## List of Square Numbers

Go through the list of squares for numbers less than here.

## Odd and Even Square Numbers

- Squares of even numbers are even, i.e..
- Squares of
**odd numbers**are odd, i.e.. - Since every odd square is of the form the odd numbers that are of the form are not square numbers.

## Properties of Square Numbers

The following are the properties of the square numbers:

- A number with 2,3, 7 or 8 at unit՚s place should never be a perfect square. In other words, none of the square numbers ends in 2,3, 7 or 8.
- If the number of zeros at the end is even, then the number is a perfect square number. Otherwise, we can say that number ending in an odd number of zeros is never a perfect square
- If the even numbers are squared, it always gives even numbers. Also, if the odd numbers are squared, it always gives odd numbers.
- If the natural numbers other than one is squared, it should be either a multiple of 3 or exceeds a multiple of 3 by 1.
- f the natural numbers other than one is squared, it should be either a multiple of 4 or exceeds a multiple of 4 by 1.
- It is noted that the unit՚s digit of the square of a natural number is equal to the unit՚s digit of the square of the digit at unit՚s place of the given natural number.
- There are n natural numbers, say p and q such that
- For every natural number n, we can write it as:
- If a number n is squared, it equals to the sum of first n odd natural numbers.
- For any natural number, say “n” which is greater than 1, we can say that should be a Pythagorean triplet.