1. **State the problem:** Simplify the square root of 674, i.e., find $\sqrt{674}$ in simplest radical form. 2. **Recall the formula and rules:** To simplify $\sqrt{n}$, find the largest perfect square factor of $n$ and use the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. 3. **Factor 674:** $$674 = 2 \times 337$$ 337 is a prime number, so no further factorization into perfect squares is possible. 4. **Check for perfect square factors:** Neither 2 nor 337 is a perfect square. 5. **Conclusion:** Since 674 has no perfect square factors other than 1, $\sqrt{674}$ is already in simplest form. **Final answer:** $$\sqrt{674}$$