1. **State the problem:** Simplify the expression $\left(\sqrt{17.8}\right)^2$. 2. **Recall the formula:** The square of a square root simplifies as $\left(\sqrt{x}\right)^2 = x$ for any non-negative $x$. 3. **Apply the formula:** $$\left(\sqrt{17.8}\right)^2 = 17.8$$ 4. **Explanation:** Squaring a square root cancels the root, leaving the original number inside the root. 5. **Final answer:** $$17.8$$