Naive way of obtaining square roots with newton's approximation method

newtonsqrt.go

package main

import (
	"fmt"
	//"math"
)

func main() {
	const (
		x0      = 54777
		epsilon = 1.0e-15
	)

	var (
		result = 0.0
		xi     = 1.0
		delta  = 1.0
	)

	for delta >= epsilon {
		result = ((xi * xi) + x0) / (2 * xi)
		delta = result - xi
		xi = result
		if delta < 0 {
			delta = -delta
		}
	}
	fmt.Println(result)
	//fmt.Println(math.Sqrt(x0))
}

Excellent!!!

package main

import (
	"fmt"
	"math"
)

func Sqrt(x float64) float64 {
	z := 1.0
	// First guess
	z -= (z*z - x) / (2*z)
	// Iterate until change is very small
	for zNew, delta := z, z; delta > 0.00000001; z = zNew {
		zNew -= (zNew * zNew - x) / (2 * zNew)
		delta = z - zNew
	}
	return z
}

func main() {
	fmt.Println(Sqrt(2))
	fmt.Println(math.Sqrt(2))
}

package main

import (
	"fmt"
	"math"
)

func Sqrt(x float64) float64 {
	var zi float64 = x/2
	delta := 0.00000001
	z := zi - (zi*zi - x) / (2*zi)
	
	for math.Abs(z-zi) > delta {
		zi = z
		z -= (zi*zi - x) / (2*zi)
		fmt.Printf("%v, %v\n", zi, z)
	}
	return z
}

func main() {
	fmt.Println(Sqrt(0.5))
	fmt.Println("real value = " + fmt.Sprint(math.Sqrt(0.5)))
}