1. **State the problem:** We need to find the value of $x$ in a square where the diagonal length is given as 8. 2. **Recall the formula:** For a square with side length $x$, the diagonal $d$ is given by the Pythagorean theorem: $$d = x\sqrt{2}$$ This is because the diagonal forms a right triangle with two sides of length $x$. 3. **Set up the equation:** Given $d = 8$, we have $$8 = x\sqrt{2}$$ 4. **Solve for $x$:** Divide both sides by $\sqrt{2}$: $$x = \frac{8}{\sqrt{2}}$$ 5. **Simplify the expression:** Rationalize the denominator: $$x = \frac{8}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{8\sqrt{2}}{2}$$ 6. **Simplify the fraction:** $$x = 4\sqrt{2}$$ 7. **Calculate the numerical value:** $$x \approx 4 \times 1.414 = 5.656$$ 8. **Round to the nearest tenth:** $$x \approx 5.7$$ **Final answer:** The side length $x$ is approximately **5.7**.