Approximating Square Root: Newton's Method

Find	√90 (= 9.486832981)
Solve	x2 = 90 or f(x) = x2 - 90
Need	f'(x) = 2x

Iterative Approach: Improve a solution x_n by computing x_n+1 = x_n - f(x_n)/f'(x_n)

Starting Point (initial guess): x₀ = 9
x₁ = 9 - (9² - 90)/2 × 9 = 9.5
x₂ = 9.5 - (9.5² - 90)/2 × 9.5 = 9.486842105.5