If a number n is odd, what can we say about n^2?
Correct Answer: n^2 is odd
- Step 1: Understand what an odd number is. An odd number is any integer that cannot be divided evenly by 2. Examples include 1, 3, 5, 7, etc.
- Step 2: When we square a number, we multiply it by itself. For example, if n is an odd number, then n^2 means n * n.
- Step 3: Let's take an example of an odd number, like 3. If we square it, we get 3 * 3 = 9, which is also odd.
- Step 4: Now, let's try another odd number, like 5. Squaring it gives us 5 * 5 = 25, which is also odd.
- Step 5: We can see that squaring different odd numbers always results in another odd number.
- Step 6: Therefore, we can conclude that if n is an odd number, then n^2 (the square of n) is also odd.
- Odd Numbers – An odd number is an integer that is not divisible by 2, typically represented in the form of 2k + 1, where k is an integer.
- Properties of Squares – The square of any integer retains the parity of the original integer; thus, the square of an odd number is also odd.
