The "divide and average" method, an old$-$time method for approximating the square root of any positive

number a can be formulated as

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

Design a function that accepts a$,$ es$,$ and maxlterations to implement this method. Use a while loop to

calculate the root approximation $x_i$ with the stopping criterion ${}_s$ or iteration $$ maxiterations. Assume the

initial value of $x_i$ to be $\frac{a}{2}.$ Estimate the error in your approximation as:

$=|\frac{x_{\text{n}\text{e}\text{w}}-x_{\text{o}\text{l}\text{d}}}{x_{\text{n}\text{e}\text{w}}}|$

Return the final root approximation, ea$,$ and iter. Test your function with $a=25,$ es $=0\mathrm{.}001,$ and maxiterations

$=50.$

output:

xi$=5$

ea $=$

$3\mathrm{.}355538069627073e-10$

iter $=6)$

PLease find matlab code to have the same as the output