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If a number n is odd, what can we say about n^2?

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Question: If a number n is odd, what can we say about n^2?

Options:

  1. n^2 is even
  2. n^2 is odd
  3. n^2 is prime
  4. n^2 is composite

Correct Answer: n^2 is odd

Solution: 

The square of an odd number is always odd.

If a number n is odd, what can we say about n^2?

Practice Questions

Q1
If a number n is odd, what can we say about n^2?
  1. n^2 is even
  2. n^2 is odd
  3. n^2 is prime
  4. n^2 is composite

Questions & Step-by-Step Solutions

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.
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