Solve square root of 7 using Newton raphson method.

Question

Newton raphson of Square root of 7

Answer 1

It is not clear how accurate that you want the approximation. There is a techniques where you just find the linear estimation of a function from a point nearby that you know (In this example you know sqrt(9) or sqrt(4).

To use the full method to arbitrary precision, you can apply the method to finding the zero of x²-7 = f(x)

For each iteration: x_n+1 = x_n - f(x_n)/f'(x_n)

I would start with x₀ = 2 ot 3 f(2) = -3 and f'(x) = 2x , so f'(2) = 4

The first iteration would yield x₁ = 2 - (-3/4) = 2.75

Continue for more accuracy.