The problem you’ve shared shows a square with a diagonal labeled $\sqrt{3}$ and a side of the square labeled $x$. To find the length of side $x$, we can use the relationship between the side length and the diagonal of a square.

For a square, the diagonal $d$ is related to the side length $s$ by the formula: $d = s\sqrt{2}$ Here, the diagonal is given as $\sqrt{3}$, so we can set up the equation: $\sqrt{3} = x\sqrt{2}$ Now, solve for $x$ by dividing both sides of the equation by $\sqrt{2}$: $x = \frac{\sqrt{3}}{\sqrt{2}}$ To simplify this expression and rationalize the denominator, multiply both the numerator and the denominator by $\sqrt{2}$: $x = \frac{\sqrt{3} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{\sqrt{6}}{2}$

Thus, the length of side $x$ is $\frac{\sqrt{6}}{2}$.

Would you like more details or a step-by-step breakdown of this process?

Here are some related questions you may find interesting:

1. What is the relationship between the side length and diagonal in a square?
2. How do we rationalize the denominator of a fraction involving square roots?
3. How does this formula apply to other shapes, like rectangles or rhombuses?
4. What is the value of $\frac{\sqrt{6}}{2}$ as a decimal?
5. Can this approach be used for other polygons like equilateral triangles?

Tip: When working with square roots, it’s often helpful to simplify the expression as much as possible by rationalizing the denominator!