$3\mathrm{.}13$ The $$divide and average$$ method, an old$-$time method

for approximating the square root of any positive number a$,$

can be formulated as

x $=$ x $+$ a$/$x

$2$

Write a well$-$structured M$-$file function based on the

while...break loop structure to implement this algo$-$

rithm. Use proper indentation so that the structure is clear. At

each step estimate the error in your approximation as

$\backslash$epsi $=$

$$

$$

$$

$$

x new $$ x old

x new

$$

$$

$$

$$

Repeat the loop until $\backslash$epsi is less than or equal to a specified

value. Design your program so that it returns both the result

and the error. Make sure that it can evaluate the square root

of numbers that are equal to and less than zero. For the latter

case, display the result as an imaginary number. For exam$-$

ple, the square root of $4$ would return $2$i$.$ Test your program

by evaluating a $=0,2,10$ and $4$ for $\backslash$epsi $=1\backslash$times $104$