Hippocampus Algebra: Divide and average method

Last time we learned how to find square roots by guess and check method. Let's take a quick review.

Find the square root of the given number to three decimal places.

After entering your answer, click the “Submit” button.

Now, let's move on with today's lesson.

The ancient Babylonians invented a method for finding square roots almost 4,000 years ago.

It’s known as the divide and average method.

This method has four steps. First, we make a guess at the square root of the number.

Next, we divide the number by our guess.

Then, we average this number and our previous guess.

Finally, use this average as our next guess.

We repeat this process until we have a square root of the desired accuracy.

Let’s find the <EQUATION>.

Our first guess is <EQUATION>, because <EQUATION>, which is close to our number.

We find that &space; &space; &space; &space; &space; &space; <EQUATION>.

Next, we find the average of this number and 21.

This gives 21.2143.

This number squared gives slightly more than 450.

Now, let’s repeat the process with our latest guess.

Which number is our next guess? Click the “Submit” button after entering your answer.

After going through the divide and average process, we get 21.2132 as our next guess.

If we square this number, we get 450.000 rounded to three decimal places.

We can stop here. We found that the <EQUATION>.

We only had to go through the divide and average process twice.

Now, let’s find the <EQUATION>.

First, we make an initial guess of 31.

<EQUATION>, so it’s a good first guess.

Next, we divide 1000 by 31. This gives 32.2581.

Averaging this number and 31 gives 31.6291.

We use this as our next guess.

Now, go through the divide and average process two more times.

What is the value of the <EQUATION> that you find? Give your answer to four decimal places. Click the “Submit” button after entering your answer.

We find that the <EQUATION>, when rounded to four decimal places.

In the next lesson, we will look at yet another method for finding square roots.