Numerical Methods: Recursive Square Root

Numerous algorithms exist for determining the square root of a non-negative real number. An interesting one that can be derived from Newton's Method, involves starting with an initial guess followed by successive refinements.

For example, suppose the square root of a number, n, is sought. Taking an initial guess g₀, we would have our answer if g₀² was sufficiently close to n, say,

|n-g₀²|< 0.001

If it is not, we could use the average of g and n/g₀, call it  g₁, and try again.  As a result, our feedback strategy should reveal a sequences of closer approximations to the square root of n.

Task: Write a recursive function,

float sqrt(float n, float g)

that will return an approximation to the square root of n, accurate to 0.001. 

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