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Help Me

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

Nov 25, 2018

#1
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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.

Nov 25, 2018
#2
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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....!!!!   Nov 25, 2018