SICP method to find squareRoot

Suppose such a program to find square-root:

def sqrt(x):
    return sqrt_iter(1, x)
def sqrt_iter(guess, x):
    if x < 0: raise ValueError("n must not be negative.")
    while True:
        if good_enough_p(guess, x):
            return guess
        else:
            guess = improve(guess, x) def improve(guess, x):
    return average(guess, x/guess)
def good_enough_p(guess, x):
    return abs(guess**2 - x) < 0.00001
def average(x, y):
    return (x + y) / 2

I tried to re-write it in java as:

public class Newton {
    public static double sqrt(double x) {
        return sqrtIter(1, x);
    }
    public double sqrtIter(double guess, double x) {
        if (x < 0) {
            throw new IllegalArgumentException("x must not be negative.");
        }
        while (true) {
            if (goodEnough(double guess, double x)) {
                return guess;
            } else {
                guess = improve(guess, x);
            }
        }
        public double improve(double guess, double x) {
            return average(guess, x/guess);
        }
        public double average(double x, double y) {
            return (x + y) / 2;
        }
        public boolean goodEnough(double guess, double x) {
            return Math.abs(guess*guess -x) < 0.0001;
        }
    }
}

However, it report 6 errors:

Newton.java:10: error: '.class' expected
            if (goodEnough(double guess, double x)) {
                                  ^
Newton.java:10: error: ';' expected
            if (goodEnough(double guess, double x)) {
                                       ^
Newton.java:10: error: ';' expected
            if (goodEnough(double guess, double x)) {
                                                 ^
Newton.java:12: error: 'else' without 'if'
            } else {
              ^
Newton.java:16: error: illegal start of expression
        public double improve(double guess, double x) {
        ^
Newton.java:26: error: class, interface, or enum expected
}
^
6 errors

I' afraid that have to finish reading a book such as Core-Java-Volumn before could correct them.

Could you please give some hints to correct the program?

Overall your translation with java was almost fine.
The issues were that you need an instance and remove types when call a method.

public class Newton {
	public static void main(String args[]) {
		Newton instance = new Newton();
		System.out.println(instance.sqrt(4.33));
	}

	public double sqrt(double x) {
		return sqrtIter(1, x);
	}

	public double sqrtIter(double guess, double x) {
		if (x < 0) {
			throw new IllegalArgumentException("x must not be negative.");
		}
		while (true) {
			if (goodEnough(guess, x)) {
				return guess;
			} else {
				guess = improve(guess, x);
			}
		}
	}

	public double improve(double guess, double x) {
		return average(guess, x / guess);
	}

	public double average(double x, double y) {
		return (x + y) / 2;
	}

	public boolean goodEnough(double guess, double x) {
		return Math.abs(guess * guess - x) < 0.0001;
	}

}

Output

2.080865423875971

in java static context can be called from static context only .

try

public class Newton {
    public static double sqrt(double x) {
        return sqrtIter(1, x);
    }
    public static double sqrtIter(double guess, double x) {
        if (x < 0) {
            throw new IllegalArgumentException("x must not be negative.");
        }
        while (true) {
            if (goodEnough( guess,  x)) {
                return guess;
            } else {
                guess = improve(guess, x);
            }
        }
        
    }
    static public double  improve(double guess, double x) {
        return average(guess, x/guess);
    }
    static public double   average(double x, double y) {
        return (x + y) / 2;
    }
    static public boolean  goodEnough(double guess, double x) {
        return Math.abs(guess*guess -x) < 0.0001;
    }
}