Mechanic's Rule The Mechanic's Rule for approximating √a, a > 0, is

where x₁, is an approximation of √a.

(a) Use Newton's Method and the function ƒ(x) = x² - a to derive the Mechanic's Rule.

(b) Use the Mechanic's Rule to approximate √5 and √7 to
three decimal places.

Xn+1 = 1/(X + X n n = 1, 2, 3 ...