A square of side \[3\] units is constructed with one side on the number line from \[0\] to \[3\]. An arc is drawn with centre at the origin and radius equal to the diagonal of the square, cutting the number line on the right at point \[X\]. Which irrational number does the point \[X\] represent? Choose 1 answer: A \[sqrt(18)\] B \[sqrt(3)\] C \[3\] D \[9\]

The problem states that the square has a side of 3 units.
So, the side length $s = 3$.

For a square with side length $s$, the length of the diagonal $d$ can be found using the Pythagorean theorem:
$d^2 = s^2 + s^2$
$d^2 = 2s^2$
$d = \sqrt{2s^2}$
$d = s\sqrt{2}$
Substitute $s = 3$:
$d = 3\sqrt{2}$

The problem states that the arc is drawn with a radius equal to the diagonal of the square.
So, the radius $R = d = 3\sqrt{2}$.

The arc is drawn with the center at the origin (0) and cuts the number line on the right at point $X$. This means the distance from the origin to point $X$ is equal to the radius.
Therefore, the point $X$ represents the value $3\sqrt{2}$ on the number line.

We need to find which option is equivalent to $3\sqrt{2}$.
Let's evaluate option A: $\sqrt{18}$
$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$

Since $X = 3\sqrt{2}$ and $\sqrt{18} = 3\sqrt{2}$, point $X$ represents the irrational number $\sqrt{18}$.