Here's another method: Babylonian method of guess and divide
My only problem with this method is=> division. How long would it take to a 6th grader to divide 20 by 4.4048 without a calculator?
Finding the square root of 20 using Babylonian method of guess and divide:>
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 |
For me, algorithm works best.
Squre root of 645 (the result is above the square root symbol)
2 | 5 | . 3 | 9 | |
√6 | .45 | .00 | .00 | |
- 4 | ||||
(45) | 2 | 45 | ||
- 2 | 25 | |||
(503) | 20 | 00 | ||
- | 15 | 09 | ||
(506_) | 4 | 91 | 00 |
Here's a method......"divide and average"..........http://mathforum.org/library/drmath/view/52623.html
Here's a website that explains it very well:>
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
I've seen your method before too, civonamzuk.....however, for my money....."divide and average" seems easier.......!!!
I suppose it's all a matter of preference......
Here's another method: Babylonian method of guess and divide
My only problem with this method is=> division. How long would it take to a 6th grader to divide 20 by 4.4048 without a calculator?
Finding the square root of 20 using Babylonian method of guess and divide:>
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 |
For me, algorithm works best.
Squre root of 645 (the result is above the square root symbol)
2 | 5 | . 3 | 9 | |
√6 | .45 | .00 | .00 | |
- 4 | ||||
(45) | 2 | 45 | ||
- 2 | 25 | |||
(503) | 20 | 00 | ||
- | 15 | 09 | ||
(506_) | 4 | 91 | 00 |