To estimate a square root to the nearest tenth, follow these steps:

1. Identify the two closest perfect squares around the number you’re finding the square root for. For example, if you need to estimate $\sqrt{20}$, the closest perfect squares are $16$ and $25$ since $4^2 = 16$ and $5^2 = 25$.

2. Determine where your number falls between these perfect squares. For $\sqrt{20}$, it falls closer to $16$ but still between $4$ and $5$.

3. Estimate by finding a midpoint between the two whole numbers. For $\sqrt{20}$, we know it’s between $4$ and $5$, and because it’s closer to $4.5$, we can start with that. Calculating $4.5^2$ yields $20.25$, which is very close to $20$.

4. Adjust your estimate if needed. Since $20.25$ is slightly above $20$, we know $\sqrt{20} \approx 4.5$.

5. Round to the nearest tenth if the number you find isn’t exact. In this case, we found that $\sqrt{20} \approx 4.5$, so our estimate to the nearest tenth is $4.5$.

This process involves approximating by narrowing down where the square root lies between whole numbers, then using midpoints and checking squares until you get a close answer.

Would you like a worked example or have further questions?

Related Questions

1. How can I estimate square roots for numbers that aren’t close to perfect squares?
2. How can I use this method for square roots between larger numbers?
3. How does the decimal place accuracy change with more precise approximations?
4. Is there a faster mental way to estimate square roots?
5. What other methods exist for estimating square roots?

Tip: For faster estimates, learn the squares of numbers from 1 to 10, as they provide a good benchmark for many square root estimations.