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How to find square root like sqrt( 2) in approximate. I don't know so pleae help me

Guest Nov 25, 2018
 #1
avatar+27219 
+1

There are several ways to find the approximate value of the square root of a number.  One of the simplest is to use Newton's method.  If you want to find the square root of N, start with an initial guess x0, then iterate using the following:  

 

xn+1 = (xn + N/xn)/2    where n is the iteration number. (i.e.   n = 0, 1, 2, 3, ... etc.)

 

Continue iterating until the result is as accurate as desired.

Alan  Nov 25, 2018
 #2
avatar+92429 
+1

Thanks, Alan

 

Here's another method...."divide and average"

 

Since 1.5^2 = 2.25.....Let   us guess that the square root of 2   =  1.5    

[ This is arbitrary....we could pick another value, if we wished....the method will still work ]

 

Divide    2 /1.5    =  1.33

Average this with  1.5    =  [ 1.33 + 1.5] / 2   = 1.415

 

Divide   2 / 1.415   =  1.4134

Average this with 1.415  =  [ 1.415 + 1.4134 ] / 2   = 1.4142

 

Divide  2 / 1.4142   =  1.4142

 

We can stop here.....this = √2   to  4 decimal places....!!!!

 

 

cool cool cool

CPhill  Nov 25, 2018

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