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What is a square number? Mention it's properties.
Square Numbers:
When a number is multiplied by itself, the product is called a ‘Square Number’.
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.
- If 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.
For example,
$12^2 = 144$, here, unit digit of $12^2$ is 4 and unit digit of $2^2$ is also 4.
1 2 2 = 144 12^2=144 1 2 2 = 144 12^2=144 - For every natural number n, we can write it as $(n+1)^2 - n^2 = (n+1)+n$
( n + 1 ) 2 − n 2 = ( n + 1 ) + n (n+1)^2-n^2=(n+1)+n - If a number n is squared, it equals to the sum of first n odd natural numbers.
- For any natural number n which is greater than 1, (2n, n^2 - 1, n^2 + 1) is a Pythagorean triplet.
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