Question

what is the formula of N-R method to find
Square root of Constant value.​

Answer 1

Given :  N-R  ( newton Raphson) method

To Find : Square root

Solution:

here  explaining it with an example

taking square root of 30

x² =  30

f(x) =  x² - 30

f'(x) = 2x

x₀  = 5  or 6

xₙ₊₁  = xₙ ​− f(xₙ​) / f'(xₙ​)​.

x₁  =  5 -   ( 5² - 30) /(2 * 5)         or 6  -  ( 6² - 30) /(2 * 6)     = 5.5

x₁  =   5 +  1/2

x₁  =   5.5

we take x₀  = 5  or 6  x₁  is same 5.5

x₂ =  5.5  -   ( 5.5² - 30) /(2 * 5.5)

x₂ =   5.5  -  0.0227

x₂  =  5.4773

x₃ =  5.4773  -   ( 5.4773² - 30) /(2 * 5.4773)

x₃ =   5.4773  -  0.00007

x₃  =  5.47723

x₄=  5.47723  -   ( 5.47723² - 30) /(2 * 5.47723)

x₄ =   5.47723 -  0.000006

x₄  =  5.477224

√30 = 5.477  

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