- #1
winsome
- 1
- 0
show that the square of any odd integer is odd, use this fact to justify the statement "if p2
is even , then p is also even
is even , then p is also even
The square of an odd integer is the result of multiplying the integer by itself. For example, the square of 3 is 9 because 3 multiplied by 3 equals 9.
To calculate the square of an odd integer, simply multiply the integer by itself. For example, to find the square of 5, you would multiply 5 by 5, which equals 25.
The square of an odd integer is always odd because when an odd number is multiplied by itself, the result will always have an odd number of factors. This is because odd numbers cannot be evenly divided by 2, so the only factors are 1 and the number itself.
This statement means that if the square of a number is even, then the number itself must also be even. In other words, if P is any odd integer, then P2 (the square of P) will always be an even number.
This statement can be justified using the properties of even and odd numbers. Since the square of an odd number is always odd, the only way for P2 to be even is if P is also even. This is because an even number multiplied by an even number will always result in an even number.