$2\mathrm{.}7$ The "divide and average" method, an old$-$time method for approximating the square root of any positive number $a,$ can be formulated as

$x=\frac{x+\frac{a}{x}}{2}$

$($a$)$ Write well$-$structured pseudocode to implement this algorithm as depicted in Fig. P$2\mathrm{.}7.$ Use proper indentation so that the structure is clear.

$($b$)$ Develop, debug, and document a program to implement this equation in either a high$-$level language or a macro language of your choice. Structure your code according to Fig. P$2\mathrm{.}7.$

FIGURE P$2\mathrm{.}7$