Implementing Square root function

I got this question in my Assembly lab. I had to code this up for 8086 processor. But I’ll be writing about the approach here.

If `r` is the square root of `X`, then r*r == X.

We can use the binary search aproach to search for this number `r`, since it would lie between [1,X].

Thus, if r*r< X, then we can search for the number in upper right of the function?

If r*r > X, then we should expect the square root to be on the left side of the function?

lower_bound = 0
upper_bound = len(A)
while lower_bound < upper_bound:
        mid = (lower_bound+upper_bound)/2
        if mid*mid == A:
            return mid
        if mid*mid < A:
            lower_bound = mid+1
            ans = lower_bound
        if mid*mid > A:
            upper_bound = mid-1
    return ans