Newton’s method for solving roots takes an estimate of the value of the root and tests it for accuracy. If the guess does not meet the required tolerance, it computes a new estimate and repeats. Pseudo-code for using Newton’s method to get the square root of a number is:

function root-by-newtons-method (x, tolerance)

guess := 1;

repeat guess := 1/2(guess + x/guess)

until absolute-value(x − guess * guess) < tolerance Write a recursive LISP function to compute square roots by Newton’s method.