Question

*Will fan and medal!* Larry wants to use the Babylonian method to estimate the square root of 71 to the nearest hundredth. His initial estimate is 8.2. What is his estimate after he correctly completes the Babylonian method once? Explain please.

Answer 1

This other way is called Babylonian method of guess and divide, and it truly is faster. It is also the same as you would get applying Newton's method. See for example finding the square root of 20 using 10 as the initial guess:

Guess Divide Find average
10 20/10 = 2 average 10 and 2 to give new guess of 6
6 20/6 = 3.333 average 3.333 and 6 gives 4.6666
4.666 20/4.666= 4.1414 average 4.666,4.1414= 4.4048
4.4048 20/4.4048=4.5454 average = 4.4700
4.4700 20/4.4700=4.4742 average = 4.4721
4.4721 20/4.4721=4.47217 average = 4.47214
This is already to 4 decimal places
4.47214 20/4.47214=4.472132 average =4.472135
4.472135 20/4.472135=4.472137 average = 4.472136

Answer 2

Take the average of "8.2" and "71/8.2"

Answer 3

how do i find the average? It's probably really simple isn't it.

Answer 4

The average of a and b is (a+b)/2

Answer 5

Ok I think I get it now, thanks.

Answer 6

No problem