#4**+5 **

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 |

civonamzuk Jun 18, 2015

#1**+5 **

Here's a method......"divide and average"..........http://mathforum.org/library/drmath/view/52623.html

CPhill Jun 18, 2015

#2**+5 **

Here's a website that explains it very well:>

http://www.homeschoolmath.net/teaching/square-root-algorithm.php

civonamzuk Jun 18, 2015

#3**0 **

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......

CPhill Jun 18, 2015

#4**+5 **

Best Answer

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 |

civonamzuk Jun 18, 2015