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$$\mathrm{ERROR}$$how do you calculate a square root by hand

 Jun 18, 2015

Best Answer 

 #4
avatar+1068 
+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:>

GuessDivideFind average
1020/10 = 2average 10 and 2 to give new guess of 6
620/6 = 3.333average 3.333 and 6 gives 4.6666
4.66620/4.666= 4.1414average 4.666,4.1414= 4.4048
4.404820/4.4048=4.5454average = 4.4700
4.470020/4.4700=4.4742average = 4.4721
4.472120/4.4721=4.47217average = 4.47214
This is already to 4 decimal places
4.4721420/4.47214=4.472132average =4.472135
4.47213520/4.472135=4.472137average = 4.472136

 

For me, algorithm works best.

Squre root of 645 (the result is above the square root symbol)

 

 2

5

. 39
 6.45.00.00
  - 4   
(45)245  
 - 225  
(503)2000 
 1509 
(506_) 49100
 Jun 18, 2015
 #1
avatar+98196 
+5

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

 

 

 

 Jun 18, 2015
 #2
avatar+1068 
+5

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

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

 Jun 18, 2015
 #3
avatar+98196 
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......

 

 

 Jun 18, 2015
 #4
avatar+1068 
+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:>

GuessDivideFind average
1020/10 = 2average 10 and 2 to give new guess of 6
620/6 = 3.333average 3.333 and 6 gives 4.6666
4.66620/4.666= 4.1414average 4.666,4.1414= 4.4048
4.404820/4.4048=4.5454average = 4.4700
4.470020/4.4700=4.4742average = 4.4721
4.472120/4.4721=4.47217average = 4.47214
This is already to 4 decimal places
4.4721420/4.47214=4.472132average =4.472135
4.47213520/4.472135=4.472137average = 4.472136

 

For me, algorithm works best.

Squre root of 645 (the result is above the square root symbol)

 

 2

5

. 39
 6.45.00.00
  - 4   
(45)245  
 - 225  
(503)2000 
 1509 
(506_) 49100
civonamzuk Jun 18, 2015

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