Square Root Recursive Problem

I am trying to write a function to express this but I keep confusing myself. Maybe I am thinking about it too hard?

4.5 is halfway between 1 and 8. 4.52 = 20.25, so the square root of 8 must be less than 4.5.
2.75 is halfway between 1 and 4.5. 2.752 = 7.5625, so the square root of 8 must be greater than 2.75.
3.625 is halfway between 2.75 and 4.5. 3.6252 = 13.140625, so the square root of 8 must be less than 3.625.
(and so on…)
Continuing this process long enough reveals that the square root of 8 is about 2.828.

My code is messed up somewhere because I keep getting back the same number that I scanned in. This is what I have so far:

Code:

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#include <stdio.h>
#include <math.h>

double recursive_square (double n);

int main (void)
{
    double num = 0;
    double result = 0;
   
   
    printf("Enter a number to compute the square root of:\n");
    scanf("%lf", &num);
   
    result = recursive_square(num);
   
    printf("The square root of %lf is about %.3lf \n", num, result);
   
    system ("PAUSE");
    return 0; 
}

double recursive_square (double n)
{
    double tempval = n/2;
   
    do
    {
        // If x2 is bigger than n, then we know that the square
        //root of n must be between 1 and x,
        if ((tempval*tempval) > n)
        {
            tempval /= 2;
        }
        //otherwise it's between x and n
        if (tempval * tempval < n)
        {
            tempval += (n - tempval);
        }
    } while (((n - tempval) >= .001) || ((tempval - n) >= .001));
   
    return tempval;
}

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my gut feeling is that you need 3 pieces of information. the number you want to square root, a lower bound and an upper bound. so for example

1^2 < 8 < 8^2

so you could pass these into a recursive function eg

Code:

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recursiveFunction(8, 1, 8)

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that function could then perform this logic

Code:

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4.5 is halfway between 1 and 8. 4.52 = 20.25, so the square root of 8 must be less than 4.5.

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and then it could perform this call

Code:

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recursiveFunction(8, 1, 4.5)

---

so now the upper bound has been reduced

right now your using a loop which works fine but so its not quite recursive since you dont call the same function from within itself.

You need a base case, to return when you decide your apprimation is good enough. In this case, you return that approximation and you are done. Then you need two branches - if the approximation is too low, return the function called with the upper half of your interval. If the approximation is too high, return the function called with the lower half of your interval.

A better way to revise your estimate is to use the value half way between tempval and n/tempval