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# how do you calculate a square root by hand

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456
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$$\mathrm{ERROR}$$how do you calculate a square root by hand

Guest Jun 18, 2015

#4
+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:>

 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
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#1
+85809
+5

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

CPhill  Jun 18, 2015
#2
+1068
+5

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

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

civonamzuk  Jun 18, 2015
#3
+85809
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
+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:>

 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

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