This is a small program I’ve come up with, with the intention of finding the root of a perfect square. I wanted some comments on the performance impact, as well as the use of resources.

square_root.c 
#include "square_root.h"

static uint64_t power(uint8_t base, uint8_t exp) {
    uint64_t result = 1;

    while (exp--) {
        result *= base;
    }

    return result;
}

static uint64_t seed(uint64_t radicand) {
    uint64_t a = radicand;
    uint64_t n = 0;

    while (radicand /= 100) {
        a = radicand;
        ++n;
    }

    return ((a < 10)
        ? ((0.28 * a) + 0.89)
        : ((0.089 * a) + 2.8)) * power(10, n);
}

static uint64_t heron(uint64_t x, uint64_t s) {
    while (s != power(x, 2)) {
        x = (x + (s / x)) / 2;
    }

    return x;
}

uint16_t square_root(uint64_t radicand) {
    return heron(seed(radicand), radicand);
}
square_root.h 
#ifndef SQUARE_ROOT_H
#define SQUARE_ROOT_H

#include <stdbool.h>
#include <stdint.h>
#include <stddef.h>

uint16_t square_root(uint64_t radicand);

#endif