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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