P$3.$ The 'divide and average' method, an iterative method for obtaining the square root of a positive number $a,$ can

be formulated as:

$x_{i+1}=\frac{(x_i+\frac{a}{x_i})}{2}$

where the subscript i indicates iteration $i$ to $i+1.$ Write a PYTHON program based on a while loop to

implement this algorithm and then find the square root of $21,$ correct up to five significant digits. Use the

approx. relative error criterion to assess convergence. Note, the approx. relative error in this case is defined as

$ea=|\frac{x_{i+1}-x_i}{x_{i+1}}|100\%.$

Hint: You have to pick an initial value of $x.$ A simple and effective guess could be $x=\frac{a}{2}.$