Question

The square of odd number are _______

Answer 1

Answer:

always odd ........ correct answer

Answer 2

Answer:

✑ Odd

Step-by-step explanation:

☯︎ Let N be any odd number.

➪Then N is an integer such that N = 2k+1, where k is an integer.

➪So N² = (2k+1)² = (2k+1)(2k+1) = 2k(2k+1)+1(2k+1) = 4k²+2k+2k+1 = 4k²+4k+1 = (4k+4)k+1.

✎ Let m = 4k+4.

Then N² = mk+1.

Since k is an integer, m is an integer.

So N² is odd.

This completes the proof.