Question

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Explanation:

Define the given representation

Using the Even Number Definition knowledge point

$$ a = 2k,\quad k \in \mathbb{N} $$

Square the expression

Using the Algebraic Proofs knowledge point

$$ a^2 = (2k)^2 = 4k^2 $$

Analyze divisibility by 4

Using the Algebraic Proofs knowledge point

$$ a^2 = 4(k^2) $$

Identify the proof method

Using the Direct Proof knowledge point

$$ \text{Direct Proof} $$

Determine the correct process option

The question asks: "What process can be used to prove that the square of the number is divisible by 4?"
The correct option is:
"Write an expression for any even number, square it, and show the result is divisible by 4."
This corresponds to option C.

Answer:

• (A) Write an expression for any odd number, square it, and show it is not divisible by 4.
• (B) Write an expression for any natural number, square it, and show it is not divisible by 4.
• (C) Write an expression for any even number, square it, and show the result is divisible by 4. (Correct answer)
• (D) Write an expression for any natural number, square it, and show it is divisible by 4.