Question

What is The square of an odd natural number

Answer 1

Answer:

4n^2+4n+1 cannot be divisible by two when n is an integer, and so the square of an odd number is always odd. Which could be the square of a 4 digit odd number.

Answer 2

Answer:

The square of an odd natural number is always odd

Step-by-step explanation:

We know that,

An odd number is an integer that can be written in form 2n+1, for some integer n, since an odd number will leave remainder 1 when divided by 2.

So the square of an odd number will be,

$(2n+1)^{2}$

$= 4n^{2} + 4n + 1\\= 2 (2n^{2} + 2n) + 1\\= 2k + 1$

where $k = 2n^{2} + 2n$ is an integer

Therefore, the square of any odd number will always come out to be odd.