Question

Prove that the square of an odd number is also odd.

Answer 1

Firstly take some odd numbers 1,3,5,7,11

As we all know formula of odd numbers is 2n-1

( n is the odd numbers)

2n-1= 2×1-1=1

2n-1=2×3-1=5

2n-1=2×5-1=9

2n-1=2×7-1=13

2n-1=2×11-1=21

Answer 2

Given:

Odd number which is represented in 2n-1 or 2n+1 form.

To Prove:

Prove that the square of an odd number is also odd.

Proof:

1) Odd numbers are the numbers which is nor divisible by 2 or neither the multiple of 2.

2) The general notation for the odd numbers is 2n-1 or 2n+1. We will find the square of the both equation.

3) Square the term (2n-1)²

• 4n²+1-4n

• 2(2n²-n)+1

now let 2n²-2n = N

• 2N+1

we get the form of odd numbers only.

4) Now, Square the term (2n+1)²

• 4n²+1+4n

• 2(2n²+2n)+1

now let 2n²+2n = N

• 2N+1

Again, we get the form of odd numbers only.

Hence, the square of an odd number is also odd.