Debunking the Myth: Does y=4x Always Produce Perfect Squares?

Debunking the Myth: Does y=4x Always Produce Perfect Squares?

Nadia claims that the equation y=4x will always generate a value that is a perfect square if x represents any natural number. However, this claim is incorrect. Let's explore why.

A perfect square is an integer that can be obtained by squaring another integer. For example, 9 is a perfect square because it's the result of 3 * 3.

While the equation y=4x does produce perfect squares for some natural numbers, it doesn't hold true for all. Here's a counterexample:

Let's take x = 2. Substituting into the equation:

y = 4 * 2 = 8

8 is not a perfect square. It cannot be obtained by squaring any whole number.

Therefore, Nadia's claim is false. The equation y=4x does not always generate a perfect square for all natural numbers 'x'.