1. **State the problem:** Find the square root of 19.6. 2. **Recall the formula:** The square root of a number $x$ is a value $y$ such that $$y^2 = x.$$ Here, we want to find $y$ such that $$y^2 = 19.6.$$ 3. **Estimate the square root:** Since $19.6$ is close to $20$, and we know $$\sqrt{20} \approx 4.472,$$ the square root of 19.6 will be slightly less than 4.472. 4. **Calculate the square root:** Using a calculator or approximation method, $$\sqrt{19.6} \approx 4.427.$$ 5. **Interpretation:** This means that $$4.427^2 \approx 19.6,$$ confirming our answer. **Final answer:** $$\boxed{4.427}$$