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

Guest Nov 25, 2018

#1**+3 **

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 x_{0}, then iterate using the following:

x_{n+1} = (x_{n} + N/x_{n})/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**+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....!!!!

CPhill Nov 25, 2018