One of the methods to calculate the square root of a number is Newtons method. The formula for Newtons method is shown in Figure 2-15. Write the pseudocode for a recursive algorithm to compute a square root using Newtons method. Verify your algorithm by using it to manually calculate the following test cases: squareRoot (5, 2, 0.01) and squareRoot (4, 2, 0.01). Note: in the formula, tol is an abbreviation for tolerance.

squareRoot (num, ans, tol) =

ans if | ans2 num | tol

squareRoot(num, (ans2 + num)/(2 ans), tol) otherwise