how to use the trial and error method to approximate the square root 20 to 1 decimal place 

The **trial and error method** (also known as "guess and check") involves guessing a number, squaring it, and adjusting the guess based on how close the result is to the number whose square root you're finding. In this case, you want to approximate \(\sqrt{20}\) to **1 decimal place**.

Here’s how you can do it:

### Steps:
1. **Make a first guess.** Start with a number close to \(\sqrt{20}\). Since \(\sqrt{16} = 4\) and \(\sqrt{25} = 5\), \(\sqrt{20}\) should be somewhere between 4 and 5.

2. **Square the guess** and compare it to 20.

3. **Adjust your guess** based on whether the squared result is higher or lower than 20.

4. **Continue adjusting** until you find a guess that, when squared, gives you a number close to 20 to 1 decimal place.

### Example:

1. **Try 4.5**  
   \[
   4.5^2 = 20.25 \quad \text{(slightly more than 20)}
   \]
   This is a little too high, so we need to try a smaller number.

2. **Try 4.4**  
   \[
   4.4^2 = 19.36 \quad \text{(less than 20)}
   \]
   This is a little too low, so try something between 4.4 and 4.5.

3. **Try 4.47**  
   \[
   4.47^2 = 19.9809 \quad \text{(very close to 20)}
   \]
   This is very close to 20, and it rounds to **4.5** when taken to 1 decimal place.

Thus, \(\sqrt{20} \approx 4.5\) to **1 decimal place**.

Would you like more details or have any other questions?

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how to use the trial and error method to approximate the square root 20 to 1 decimal place

Learn how to use the trial and error method to approximate the square root of 20 to 1 decimal place. This problem focuses on square root approximation through guess and check, suitable for students in Grades 6-8.

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