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If a number n is odd, what can we say about n^2?
If a number n is odd, what can we say about n^2?
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Practice Questions
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Q1
If a number n is odd, what can we say about n^2?
n^2 is even
n^2 is odd
n^2 is prime
n^2 is composite
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The square of an odd number is always odd.
Questions & Step-by-step Solutions
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Q
Q: If a number n is odd, what can we say about n^2?
Solution:
The square of an odd number is always odd.
Steps: 6
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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.
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