Part $1$: Heron$$s Method

Use the Heron$$s method inside of a while loop to estimate the square root.

$(1)$ The formula for this method is:

$+1=$

$[+$

$]$

$2$

$$ is a number for which the square root is sought

$$ is the estimated square root

$$ is the loop counter

$(2)$ Use an initial estimate of $/2$ for $0.$

$(3)$ Set the $$while$$ loop to end when the change from one estimate to the other is less

than a tolerance value of $0\mathrm{.}0001.$

$(4)$ Store the estimate, x$,$ in a dynamic array. The array can be expanded using the

following command